Factors and connected induced subgraphs

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Let G be a connected graph without loops and without multiple edges, and let p be an integer such that 0 < p < |V(G)|. Let f be an integer-valued function on V(G) such that 2 ≤ f(x) ≤ degG(x) for all x ∈ V(G). We show that if every connected induced subgraph of order p of G has an f-factor, then G has an f-factor, unless ∑x∈V(G)f(x) is odd.

Original languageEnglish
Pages (from-to)511-515
Number of pages5
JournalGraphs and Combinatorics
Issue number3
Publication statusPublished - 1 Jan 2001


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