Title:	Perfect matchings in highly cyclically connected regular graphs
Authors:	Lukoťka, Robert Rollová, Edita
Citation:	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
Issue Date:	2022
Publisher:	Wiley
Document type:	článek article
URI:	2-s2.0-85118139855 http://hdl.handle.net/11025/47312
ISSN:	0364-9024
Keywords in different language:	2‐factor;cyclic connectivity;perfect matching;regular graph
Abstract in different language:	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.
Rights:	Plný text není přístupný. © Wiley
Appears in Collections:	Články / Articles (KMA) OBD

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.