Abstract.
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)≤ deg G (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.
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Received: June 29, 1998¶Final version received: July 30, 1999
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Kotani, K. Factors and Connected Induced Subgraphs. Graphs Comb 17, 511–515 (2001). https://doi.org/10.1007/s003730170025
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DOI: https://doi.org/10.1007/s003730170025