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1.
1-perfectly orientable K[sub]4-minor-free and outerplanar graphs
Boštjan Brešar, Tatiana Romina Hartinger, Tim Kos, Martin Milanič, 2018, original scientific article

Abstract: A graph ▫$G$▫ is said to be 1-perfectly orientable if it has an orientation ▫$D$▫ such that for every vertex ▫$v \in V(G)$▫, the out-neighborhood of ▫$v$▫ in ▫$D$▫ is a clique in ▫$G$▫. D. J. Skrien [J. Graph Theory 6, 309--316 (1982)] posed the problem of characterizing the class of 1-perfectly orientable graphs. This graph class forms a common generalization of the classes of chordal and circular arc graphs; however, while polynomially recognizable via a reduction to 2-SAT, no structural characterization of this intriguing class of graphs is known. Based on a reduction of the study of 1-perfectly orientable graphs to the biconnected case, we characterize, both in terms of forbidden induced minors and in terms of composition theorems, the classes of 1-perfectly orientable ▫$K_4$▫-minor-free graphs and of 1-perfectly orientable outerplanar graphs. As part of our approach, we introduce a class of graphs defined similarly as the class of 2-trees and relate the classes of graphs under consideration to two other graph classes closed under induced minors studied in the literature: cyclically orientable graphs and graphs of separability at most 2.
Keywords: 1-perfectly orientable graph, ▫$K_4$▫-minor-free graph, outerplanar graph
Published in DKUM: 20.09.2022; Views: 488; Downloads: 14
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2.
Comparison of and demarcation between selected economic minor offences and economic criminal offences
Bojan Geršak, Borut Bratina, Andrej Srakar, 2015, original scientific article

Abstract: Purpose: In the article, we are discussing demarcations between selected economic minor offences and selected economic criminal offences: Fraud in Securities Trading; Abuse of Insider Information; Disclosure and Unauthorised Acquisition of Trade Secrets. By now, this topic has been given virtually no attention in legal literature. Criminal law theory has mainly addressed only the question of which criteria to use in order to recognise criminal offences amongst all unlawful actions, while on the other hand, law of minor offences has generally focused strictly on less serious unlawful actions. However, in practice, a certain action can sometimes correspond to the definition of both a criminal offence and a minor offence. Consequently, it is of the essence that the statutory elements of a particular unlawful action are precisely defined and clearly demarcated. Only this can ensure legal certainty that should be guaranteed to everyone already on the basis of the Constitution of the Republic of Slovenia. A problem arises if the statutory elements of a criminal offence and a minor offence completely overlap, which leads to legal uncertainty. Design/Methods/Approach: The research is based on a quantitative investigation in the course of which we conducted a survey in order to test our assumption. First, we used basic one sided t tests on the data from section 1 questions to try our general assumption. Afterwards, we designed three sets of factors using factor analysis in order to use them on questions from sections 2–6, 7 and 8. In the last part, we took all the designed variables and some other basic information on respondents and used them in regression models for analysis of factors that affect the opinion on adequacy of Slovenian legislation regarding sanctioning and prosecution of economic crime. Findings: With the research, we wished to obtain new knowledge on the adequate demarcation between selected economic minor offences and selected criminal offences. In practice, it is material that statutory elements of a particular unlawful action are clearly defined. On the basis of our findings we propose elimination of legal vacuum in which the chosen legal articles for minor economic offences and criminal offences overlap. Research Limitations / Implications: Limitations of the present article mostly relate to the availability of data and the willingness of state agencies for cooperation in the research. This relates to the quality of primary and secondary data, particularly to the issues related with consistency in data collection and data accuracy (unwillingness of the respondents to complete the survey and the problems of time and sectorial consistency in the definitions of individual statistical variables). Practical Implications: Results of the study can provide recommendations for the consequent changes in the studied legislation and clearer demarcation of legal articles on the chosen economic and criminal offences with the purpose of strengthening of respective legal protection. Namely, this is the only way to ensure legal certainty that should be guaranteed to everyone on the basis of the Constitution of the Republic of Slovenia. Originality/Value: Value of this article is in the empirical demonstration and normative arrangement of a specific field of law, i.e., the legislation in the field of sanctioning and prosecution of economic crime.
Keywords: economic criminal offences, economic minor offences, demarcation, legal certainty, unlawful actions
Published in DKUM: 16.04.2020; Views: 962; Downloads: 68
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3.
Crossing number additivity over edge cuts
Drago Bokal, Markus Chimani, Jesús Leanõs, 2013, original scientific article

Abstract: Consider a graph ▫$G$▫ with a minimal edge cut ▫$F$▫ and let ▫$G_1$▫, ▫$G_2$▫ be the two (augmented) components of ▫$G-F$▫. A long-open question asks under which conditions the crossing number of ▫$G$▫ is (greater than or) equal to the sum ofcthe crossing numbers of ▫$G_1$▫ and ▫$G_2$▫ - which would allow us to consider those graphs separately. It is known that crossing number is additive for ▫$|F| in {0,1,2}$▫ and that there exist graphs violating this property with ▫$|F| ge 4$▫. In this paper, we show that crossing number is additive for ▫$|F|=3$▫, thus closing the final gap in the question. The techniques generalize to show that minor crossing number is additive over edge cuts of arbitrary size, as well as to provide bounds for crossing number additivity in arbitrary surfaces. We point out several applications to exact crossing number computation and crossing-critical graphs, as well as provide a very general lower bound for the minor crossing number of the Cartesian product of an arbitrary graph with a tree.
Keywords: matematika, teorija grafov, prekrižno število, minor, mathematics, graph theory, crossing number, minor
Published in DKUM: 10.07.2015; Views: 1385; Downloads: 97
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4.
General lower bounds for the minor crossing number of graphs
Drago Bokal, Éva Czabarka, László Székely, Imrich Vrt'o, 2010, original scientific article

Abstract: Obstajajo tri splošne spodnje meje za minorsko prekrižno število grafov: prekrižna lema, metoda z bisekcijo in metoda z vložitvami. V tem prispevku predstavimo njihove prilagoditve za minorsko prekrižno število grafov. S tako pridobljenimi spodnjimi mejami izboljšamo znane rezultate za minorsko prekrižno število hiperkock. Poleg navedenih rezultatov predstavimo tudi povezavo med minorskim prekrižnim številom in grafi, predstavljivimi s krivuljami (string-graphs).
Keywords: teorija grafov, minorsko prekrižno število, grafovski minor, krivuljski grafi, hiper kocke, graph theory, minor crossing number, graph minor, string graphs, hypercubes
Published in DKUM: 10.07.2015; Views: 1075; Downloads: 99
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6.
General lower bounds for the minor crossing number of graphs
Drago Bokal, Éva Czabarka, László Székely, Imrich Vrt'o, 2008

Abstract: There are three general lower bound techniques for the crossing numbers of graphs: the Crossing Lemma, the bisection method and the embedding method. Inthis contribution, we present their adaptations to the minor crossing number. Using the adapted bounds, we improve on the known bounds on the minor crossing number of hypercubes. We also point out relations of the minor crossing number to string graphs.
Keywords: teorija grafov, prekrižno število, minor, hiper kocke, graph theory, minor crossing number, graph minor, string graphs, hypercubes
Published in DKUM: 10.07.2015; Views: 1011; Downloads: 86
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7.
Possible role of jasmonic acid in the regulation of floral induction, evocation and floral differentiation in Lemna minor L.
Božidar Krajnčič, Janja Kristl, Ignac Janžekovič, 2006, original scientific article

Abstract: Jasmonic acid (JA) is implicated in a wide variety of developmental and physiological processes in plants. Here, we studied the effects of JA and the combination of JA and ethylenediamine-dio-hydroxypheny-acetic acid (EDDHA) on flowering in Lemna minor in axenical cultures. JA (0.475-47.5 nmol l-1) enhanced floral induction in L. minor under long-day (LD) conditions. Under the same conditions, at the concentration of 237.5 nmol l-1, JA inhibited floral induction, and at the concentration of 475 nmol l-1 it prevented floral induction. Under LD conditions with LD preculture, a combination of EDDHA (20,500 nmol l-1) and JA (47.5 nmol l-1) had a synergistic effect on the promotion of floral induction. Floral induction was enhanced to the greatest extent in experiments with LD precultures. Microscopic examination of microphotographs of histological sections showed that JA and, to an even greater extent, JA+ EDDHA at optimal concentrations promote apical floral induction (evocation). Furthermore, and to an even greater extent JA in combination with EDDHA in an optimal concentration, also promote flower differentiation, especially the development of stamens, as is evident from themicrophotographs. The experimental results show that JA promotes floral induction in other species of Lemnaceae from various groups according to their photoperiodic response. The results support our hypothesis that, in addition to previosly ascribed functions, JA may regulate floral induction, evocation and floral differentiation. Our hypothesis is supported also by the results obtained by quantitative determination of endogenous JA levels in L. minor at three growth stages. The levels of endogenous JA decreased from 389 ng JA g-1 (fresh weight) of L. minor during the vegetative stage to 217 ng JA g-1 during the evocation stage, and to 37.5 ng JA g-1 during the flowering stage, which proves that JA is used for flowering.
Keywords: chelating agent EDDHA, flowering, jasmonic acid (JA), Lemna minor L., endogenous JA levels
Published in DKUM: 10.07.2015; Views: 1724; Downloads: 115
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8.
The minor crossing number of graphs with an excluded minor
Drago Bokal, Gašper Fijavž, David Richard Wood, 2008, original scientific article

Abstract: The minor crossing number of a graph ▫$G$▫ is the minimum crossing number of a graph that contains ▫$G$▫ as a minor. It is proved that for every graph ▫$H$▫ there is a constant ▫$c$▫, such that every graph ▫$G$▫ with no ▫$H$▫-minor has minor crossing number at most ▫$c|V(G)|$▫.
Keywords: mathematics, graph theory, graph minor, excluded minor, crossing number, minor crossing number
Published in DKUM: 10.07.2015; Views: 1176; Downloads: 250
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9.
Odziv male vodne leče (Lemna minor L.) na vsebnost onesnažil v vodnih vzorcih potoka Peklenščice
Tanja Krivec, 2015, master's thesis

Abstract: Namen magistrske naloge je bil ugotoviti odvisnost vsebnosti nekaterih onesnažil v vodi potoka Peklenščica od vrste dejavnosti v zaledju in od vremenskih razmer. Pri tem smo osnovne fizikalno-kemijske analize dopolnili s testom strupenosti z malo vodno lečo (Lemna minor). Vodni vzorci so bili odvzeti na petih lokacijah od izvira potoka Peklenščica do izliva v potok Trnavo, in sicer ob štirih vzorčenjih med novembrom 2013 in avgustom 2014. V laboratoriju smo opravljali analize teh vzorcev, in sicer meritve koncentracij nitratov, nitritov, celotnega fosforja in meritve pH-vrednosti. Najvišje koncentracije hranil smo izmerili ob spomladanskem vzorčenju, ki je bilo izvedeno v času po obilnih padavinah in gnojenju na Ponikovski planoti, najnižje pa pri zimskem vzorčenju, ko gnojenja in padavin na planoti ni bilo. Odziv male vodne leče na onesnažila v vodnih vzorcih smo ocenjevali s spremljanjem njene rasti v skladu s standardom ISO 20079:2005. Klasično štetje stebelnih členkov smo nadgradili z uporabo metode računalniškega vida, pri kateri smo odčitavali površine stebelnih členkov pred in po sedemdnevni izpostavitvi vodnim vzorcem potoka Peklenščica. S tem smo odpravili napake, ki se lahko pojavijo pri štetju stebelnih členkov s prostim očesom. Spremembo v površini stebelnih členkov smo predstavili kot relativno stopnjo rasti (RGR) male vodne leče. Ugotovili smo zmanjšanje rasti po izpostavitvi vsem vodnim vzorcem potoka Peklenščica v primerjavi s kontrolo. Zmanjšanje rasti male vodne leče je eden od pokazateljev strupenosti vodnih vzorcev. Največje zmanjšanje rasti je bilo izračunano v vzorcih, odvzetih pri spomladanskem vzorčenju, najmanjše pa pri vzorcih, odvzetih v zimskem času. Izmed vseh merjenih parametrov (nitrati, nitriti, celotni fosfor in pH-vrednost) smo najvišjo stopnjo povezljivosti relativne stopnje rasti male vodne leče izračunali v povezavi s pH-vrednostmi vodnih vzorcev. Izsledki raziskave so pokazali, da je pH-vrednost odločilen limitirajoč faktor za rast male vodne leče. Pri nadaljnjih analizah bi bilo potrebno vzdrževati enake pH-vrednosti vodnih vzorcev, da bi lahko ugotovili vpliv drugih parametrov v vodi na rast male vodne leče.
Keywords: Lemna minor, test strupenosti, varstvo voda, Peklenščica, računalniški vid
Published in DKUM: 16.02.2015; Views: 2321; Downloads: 286  (1 vote)
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