Large even factors of graphs

Jing Chen () and Genghua Fan ()
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Jing Chen: Fuzhou University
Genghua Fan: Fuzhou University

Journal of Combinatorial Optimization, 2018, vol. 35, issue 1, No 13, 162-169

Abstract: Abstract A spanning subgraph F of a graph G is called an even factor of G if each vertex of F has even degree at least 2 in F. It was conjectured that if a graph G has an even factor, then it has an even factor F with $$|E(F)|\ge {4\over 7}(|E(G)| + 1)+ {2\over 7}|V_2(G)|$$ | E ( F ) | ≥ 4 7 ( | E ( G ) | + 1 ) + 2 7 | V 2 ( G ) | , where $$V_2(G)$$ V 2 ( G ) is the set of vertices of degree 2 in G. We note that the conjecture is false if G is a triangle. In this paper, we confirm the conjecture for all graphs on at least 4 vertices, and moreover, we prove that if $$|E(H)|\le {4\over 7}(|E(G)| + 1)+ {2\over 7}|V_2(G)|$$ | E ( H ) | ≤ 4 7 ( | E ( G ) | + 1 ) + 2 7 | V 2 ( G ) | for every even factor H of G, then every maximum even factor of G is a 2-factor consisting of even circuits.

Keywords: Even factor; Spanning subgraph; 2-factor; Extremal graph (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10878-017-0161-x

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