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15. On two extensions of equimatchable graphsZakir Deniz, Tinaz Ekim, Tatiana Romina Hartinger, Martin Milanič, Mordechai Shalom, 2017, original scientific article Keywords: minimum maximal matching, equimatchable graph, edge dominating set, Gallai-Edmonds decomposition, parameterized complexity
Published in RUP: 29.01.2018; Views: 2227; Downloads: 146
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16. On cyclic edge-connectivity of fullerenesKlavdija Kutnar, Dragan Marušič, 2008, original scientific article Abstract: A graph is said to be cyclically ▫$k$▫-edge-connected, if at least ▫$k$▫ edges must be removed to disconnect it into two components, each containing a cycle. Such a set of ▫$k$▫ edges is called a cyclic-k-edge cutset and it is called a trivial cyclic-k-edge cutset if at least one of the resulting two components induces a single ▫$k$▫-cycle. It is known that fullerenes, that is, 3-connected cubic planar graphs all of whose faces are pentagons and hexagons, are cyclically 5-edge-connected. In this article it is shown that a fullerene ▫$F$▫ containing a nontrivial cyclic-5-edge cutset admits two antipodal pentacaps, that is, two antipodal pentagonal faces whose neighboring faces are also pentagonal. Moreover, it is shown that ▫$F$▫ has a Hamilton cycle, and as a consequence at least ▫$15 \cdot 2^{n/20-1/2}$▫ perfect matchings, where ▫$n$▫ is the order of ▫$F$▫.
Keywords: graph, fullerene graph, cyclic edge-connectivity, hamilton cycle, perfect matching
Published in RUP: 03.04.2017; Views: 2126; Downloads: 138
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17. Regular embeddings of cycles with multiple edges revisitedKan Hu, Roman Nedela, Martin Škoviera, Naer Wang, 2015, original scientific article Abstract: Regularne vložitve ciklov z večkratnimi povezavami se pojavljajo v literaturi že kar nekaj časa, tako v topološki teoriji grafov kot tudi izven nje. Ta članek izriše kompletno podobo teh zemljevidov na ta način, da povsem opiše, klasificira in enumerira regularne vložitve ciklov z večkratnimi povezavami tako na orientabilnih kot tudi na neorientabilnih ploskvah. Večina rezultatov je sicer znana v tej ali oni obliki, toda tu so predstavljeni iz poenotenega zornega kota, osnovanega na teoriji končnih grup. Naš pristop daje dodatno informacijo tako o zemljevidih kot o njihovih grupah avtomorfizmov, priskrbi pa tudi dodaten vpogled v njihove odnose.
Keywords: regularna vložitev, večkratna povezava, Hölderjev izrek, Möbiusov zemljevid, regular embedding, multiple edge, Hölder's Theorem, Möbius map
Published in RUP: 15.10.2015; Views: 2764; Downloads: 109
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19. The impact of grazing, overgrowth and mowing on spring butterfly (Lepidoptera: Rhopalocera) assemblages on dry karst meadows and PasturesJure Jugovic, Mitja Črne, Živa Fišer, 2013, original scientific article Keywords: traditional land-use, grazing, Karst edge, Lepidoptera, Rhopalocera, habitat management
Published in RUP: 15.10.2013; Views: 3459; Downloads: 83
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20. Classification of edge-transitive rose window graphsIstván Kovács, Klavdija Kutnar, Dragan Marušič, 2010, original scientific article Abstract: Given natural numbers ▫$n \ge 3$▫ and ▫$1 \le a$▫, ▫$r \le n-1$▫, the rose window graph ▫$R_n(a,r)$▫ is a quartic graph with vertex set ▫$\{x_i \vert i \in {\mathbb Z}_n\} \cup \{y_i \vert i \in {\mathbb Z}_n\}$▫ and edge set ▫$\{\{x_i, x_{i+1}\} \vert i \in {\mathbb Z}_n\} \cup \{\{y_i, y_{i+r}\} \vert i \in {\mathbb Z}_n\} \cup \{\{x_i, y_i\} \vert i \in {\mathbb Z}_n\} \cup \{\{x_{i+a}, y_i\} \vert i \in {\mathbb Z}_n\}$▫. In this article a complete classification of edge-transitive rose window graphs is given, thus solving one of three open problems about these graphs posed by Steve Wilson in 2001.
Keywords: group, graph, rose window, vertex-transitive, edge-transitive, arc-transitive
Published in RUP: 15.10.2013; Views: 2965; Downloads: 93
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