Largest 2-Regular Subgraphs in 3-Regular Graphs

Autor:	Douglas B. West, Ringi Kim, Alexandr V. Kostochka, Ilkyoo Choi, Boram Park
Rok vydání:	2019
Předmět:	Combinatorics 010201 computation theory & mathematics Multigraph 0211 other engineering and technologies Discrete Mathematics and Combinatorics Cubic graph 021107 urban & regional planning 0102 computer and information sciences 02 engineering and technology 01 natural sciences Graph Theoretical Computer Science Mathematics
Zdroj:	Graphs and Combinatorics. 35:805-813
ISSN:	1435-5914 0911-0119
Popis:	For a graph G, let $$f_2(G)$$ denote the largest number of vertices in a 2-regular subgraph of G. We determine the minimum of $$f_2(G)$$ over 3-regular n-vertex simple graphs G. To do this, we prove that every 3-regular multigraph with exactly c cut-edges has a 2-regular subgraph that omits at most $$\max \{0,\lfloor (c-1)/2\rfloor \}$$ vertices. More generally, every n-vertex multigraph with maximum degree 3 and m edges has a 2-regular subgraph that omits at most $$\max \{0,\lfloor (3n-2m+c-1)/2\rfloor \}$$ vertices. These bounds are sharp; we describe the extremal multigraphs.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::e014418cb550c802273692a0efbfaadc https://doi.org/10.1007/s00373-019-02021-6 Zobrazit plný text záznamu Plný text ve formátu PDF Plný text ve formátu HTML
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