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http://dx.doi.org/10.4134/JKMS.j210605

SHARP ORE-TYPE CONDITIONS FOR THE EXISTENCE OF AN EVEN [4, b]-FACTOR IN A GRAPH  

Cho, Eun-Kyung (Department of Mathematics Hankuk University of Foreign Studies)
Kwon, Su-Ah (Department of Applied Mathematics and Statistics The State University of New York)
O, Suil (Department of Applied Mathematics and Statistics The State University of New York)
Publication Information
Journal of the Korean Mathematical Society / v.59, no.4, 2022 , pp. 757-774 More about this Journal
Abstract
Let a and b be positive even integers. An even [a, b]-factor of a graph G is a spanning subgraph H such that for every vertex v ∈ V (G), dH(v) is even and a ≤ dH(v) ≤ b. Let κ(G) be the minimum size of a vertex set S such that G - S is disconnected or one vertex, and let σ2(G) = minuv∉E(G) (d(u)+d(v)). In 2005, Matsuda proved an Ore-type condition for an n-vertex graph satisfying certain properties to guarantee the existence of an even [2, b]-factor. In this paper, we prove that for an even positive integer b with b ≥ 6, if G is an n-vertex graph such that n ≥ b + 5, κ(G) ≥ 4, and σ2(G) ≥ ${\frac{8n}{b+4}}$, then G contains an even [4, b]-factor; each condition on n, κ(G), and σ2(G) is sharp.
Keywords
Even [4, b]-factor; Ore-type condition; connectivity;
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Times Cited By KSCI : 1  (Citation Analysis)
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