Název:	Perfect matchings in highly cyclically connected regular graphs
Autoři:	Lukoťka, Robert Rollová, Edita
Citace zdrojového dokumentu:	LUKOŤKA, R. ROLLOVÁ, E. Perfect matchings in highly cyclically connected regular graphs. JOURNAL OF GRAPH THEORY, 2022, roč. 100, č. 1, s. 28-49. ISSN: 0364-9024
Datum vydání:	2022
Nakladatel:	Wiley
Typ dokumentu:	článek article
URI:	2-s2.0-85118139855 http://hdl.handle.net/11025/47312
ISSN:	0364-9024
Klíčová slova v dalším jazyce:	2‐factor;cyclic connectivity;perfect matching;regular graph
Abstrakt v dalším jazyce:	A leaf matching operation on a graph consists of removing a vertex of degree 1 together with its neighbour from the graph. Let G be a d‐regular cyclically (d k − 1+2 )‐ edge‐connected graph of even order, where k ≥ 0 and d ≥ 3. We prove that for any given set X of d k − 1 + edges, there is no 1‐factor of G avoiding X if and only if either an isolated vertex can be obtained by a series of leaf matching operations in G − X, or G − X has an independent set that contains more than half of the vertices of G. To demonstrate how to check the conditions of the theorem we prove several statements on 2‐factors of cubic graphs. For k ≥ 3, we prove that given a cyclically (4k − 5)‐edge‐connected cubic graphG and three paths of length k such that the distance between any two of them is at least 8k − 16, there is a 2‐factor of G that contains one of the paths. We provide a similar statement for two paths when k = 3 and k = 4. As a corollary we show that given a vertex v in a cyclically 7‐edge‐connected cubic graph, there is a 2‐factor such that v is in a circuit of length greater than 7.
Práva:	Plný text není přístupný. © Wiley
Vyskytuje se v kolekcích:	Články / Articles (KMA) OBD

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