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1.
Median and quasi-median direct products of graphs
Boštjan Brešar, Pranava Jha, Sandi Klavžar, Blaž Zmazek, 2005, izvirni znanstveni članek

Opis: Median graphs are characterized among direct products of graphs on at least three vertices. Beside some trivial cases, it is shown that one component of ▫$G \times P_3$▫ is median if and only if ▫$G$▫ is a tree in that the distance between any two vertices of degree at least 3 is even. In addition, some partial results considering median graphs of the form ▫$G \times K_2$▫ are proved, and it is shown that the only nonbipartite quasi-median direct product is ▫$K_3 \times K_3$▫.
Ključne besede: mathematics, graph theory, median graph, direct product, quasi-median graph, isometric embeddings, convexity
Objavljeno v DKUM: 31.03.2017; Ogledov: 1059; Prenosov: 373
.pdf Celotno besedilo (174,14 KB)
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2.
A generalization of Hungarian method and Hall's theorem with applications in wireless sensor networks
Drago Bokal, Boštjan Brešar, Janja Jerebic, 2012, izvirni znanstveni članek

Opis: In this paper, we consider various problems concerning quasi-matchings and semi-matchings in bipartite graphs, which generalize the classical problem of determining a perfect matching in bipartite graphs. We prove a generalization of Hall's marriage theorem, and present an algorithm that solves the problem of determining a lexicographically minimum ▫$g$▫-quasi-matching (that is a set ▫$F$▫ of edges in a bipartite graph such that in one set of the bipartition every vertex ▫$v$▫ has at least ▫$g(v)$▫ incident edges from ▫$F$▫, where ▫$g$▫ is a so-called need mapping, while on the other side of the bipartition the distribution of degrees with respect to ▫$F$▫ is lexicographically minimum). We obtain that finding a lexicographically minimum quasi-matching is equivalent to minimizing any strictly convex function on the degrees of the A-side of a quasi-matching and use this fact to prove a more general statement: the optima of any component-based strictly convex cost function on any subset of ▫$L_1$▫-sphere in ▫${mathbb N}^n$▫ are precisely the lexicographically minimal elements of this subset. We also present an application in designing optimal CDMA-based wireless sensor networks.
Ključne besede: matematika, teorija grafov, prirejanje, kvazi prirejanje, polprirejanje, tok, madžarska metoda, mathematics, graph theory, matching, quasi-matching, semi-matching, flow, Hungarian method, augmenting path
Objavljeno v DKUM: 10.07.2015; Ogledov: 1242; Prenosov: 91
URL Povezava na celotno besedilo

3.
A generalization of Hungarian method and Hall's theorem with applications in wireless sensor networks
Drago Bokal, Boštjan Brešar, Janja Jerebic, 2009

Opis: In this paper, we consider various problems concerning quasi-matchings and semi-matchings in bipartite graphs, which generalize the classical problem of determining a perfect matching in bipartite graphs. We prove a vast generalization of Hall's marriage theorem, and present an algorithm that solves the problem of determining a lexicographically minimum ▫$g$▫-quasi-matching (that is a set ▫$F$▫ of edges in a bipartite graph such that in one set of the bipartition every vertex v has at least ▫$g(v)$▫ incident edges from ▫$F$▫, where ▫$g$▫ is a so-called need mapping, while on the other side of the bipartition the distribution of degrees with respect to ▫$F$▫ is lexicographically minimum). We also present an application in designing an optimal CDMA-based wireless sensor networks.
Ključne besede: matematika, teorija grafov, prirejanje, kvazi prirejanje, polprirejanje, tok, madžarska metoda, mathematics, graph theory, matching, quasi-matching, semi-matching, flow, Hungarian method, augmenting path
Objavljeno v DKUM: 10.07.2015; Ogledov: 1139; Prenosov: 74
URL Povezava na celotno besedilo

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