1. On cyclic edge-connectivity of fullerenesDragan Marušič, Klavdija Kutnar, 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 ▫$F$▫. Found in: ključnih besedah Summary of found: ...A graph is said to be cyclically ▫$k$▫-edge-connected, if... Keywords: graph, fullerene graph, cyclic edge-connectivity, hamilton cycle, perfect matching Published: 03.04.2017; Views: 728; Downloads: 88 Full text (0,00 KB) |
2. On two extensions of equimatchable graphsZakir Deniz, Tinaz Ekim, Tatiana Romina Hartinger, Martin Milanič, Mordechai Shalom, 2017, original scientific article Found in: ključnih besedah Summary of found: ...minimum maximal matching, equimatchable graph, edge dominating set, Gallai-Edmonds decomposition,, parameterized complexity... Keywords: minimum maximal matching, equimatchable graph, edge dominating set, Gallai-Edmonds decomposition, parameterized complexity Published: 29.01.2018; Views: 576; Downloads: 94 Full text (0,00 KB) |
3. On the König deficiency of zero-reducible graphsMiklós Bartha, Miklós Ferenz Krész, 2019, original scientific article Found in: ključnih besedah Summary of found: ... graph matching, independent set, König property, graph reduction,... Keywords: graph matching, independent set, König property, graph reduction, graph algorithm Published: 14.11.2019; Views: 130; Downloads: 18 Full text (0,00 KB) |
4. On the König deficiency of zero-reducible graphsMiklós Bartha, Miklós Ferenz Krész, 2020, original scientific article Found in: ključnih besedah Summary of found: ... graph matching, independent set, König property, graph reduction,... Keywords: graph matching, independent set, König property, graph reduction, graph algorithm Published: 11.02.2020; Views: 11; Downloads: 6 Full text (0,00 KB) |