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Title:On plane bipartite graphs without fixed edges
Authors:Salem, Khaled (Author)
Klavžar, Sandi (Author)
Files:URL http://dx.doi.org/10.1016/j.aml.2006.08.014
 
Language:English
Work type:Not categorized (r6)
Typology:1.01 - Original Scientific Article
Organization:FNM - Faculty of Natural Sciences and Mathematics
Abstract:Povezava grafa ▫$H$▫, ki premore vsaj eno popolno prirejanje, je fiksna povezava, če bodisi pripada vsem popolnim prirejanjem v ▫$H$▫ bodisi nobenemu popolnemu prirejanju. Dokazano je, da je povezan, ravninski, dvodelni graf brez fiksnih povezav natanko tedaj, ko je rob vsakega lica alternirajoči cikel. Nadalje je poliheksagonalen fragment brez fiksnih povezav natanko tedaj, ko so robovi neskončnega lica in vseh nešesterokotniških lic alternirajoči cikli. Dobljeni rezultati predstavljajo razširitev rezultatov iz [F. Zhang, M. Zheng, Generalized hexagonal systems with each hexagon being resonant, Discrete Appl. Math. 36 (1992) 67-73] na posplošene haksagonalne sisteme.
Keywords:matematika, teorija grafov, popolno prirejanje, fiksna povezava, alternirajoči cikel, dvodelni ravninski graf, poliheksagonalen fragment, posplošen heksagonalen sistem, mathematics, graph theory, perfect matching, fixed edge, alternating cycle, plane bipartite graph, polyhex fragment, generalized hexagonal system
Year of publishing:2007
Number of pages:str. 813-816
Numbering:Vol. 20, no. 7
UDC:519.17:541
ISSN on article:0893-9659
COBISS_ID:14257753 Link is opened in a new window
NUK URN:URN:SI:UM:DK:RKFQ9VZX
Views:435
Downloads:50
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Categories:Misc.
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Record is a part of a journal

Title:Applied Mathematics Letters
Shortened title:Appl. math. lett.
Publisher:Pergamon
ISSN:0893-9659
COBISS.SI-ID:24984320 New window

Secondary language

Language:Unknown
Title:O ravninskih dvodelnih grafih brez fiksnih povezav
Abstract:An edge of a graph ▫$H$▫ with a perfect matching is a fixed edge if it either belongs to none or to all of the perfect matchings of ▫$H$▫. It is shown that a connected plane bipartite graph has no fixed edges if and only if the boundary of every face is an alternating cycle. Moreover, a polyhex fragment has no fixed edges if and only if the boundaries of its infinite face and the non-hexagonal finite faces are alternating cycles. These results extend results on generalized hexagonal systems from [F. Zhang, M. Zheng, Generalized hexagonal systems with each hexagon being resonant, Discrete Appl. Math. 36 (1992) 67-73].


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