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A Tutte-type characterization for graph factors by Lu, Hongliang; Wang, David G. L. is a scholarly article available to read on EtoBox.

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Let $G$ be a connected general graph. Let $f\colon V(G)\to \Z^+$ be a function. We show that $G$ satisfies the Tutte-type condition \[ o(G-S)\le f(S)\qquad\text{for all vertex subsets $S$}, \] if and only if it contains a colored $J_f^*$-factor for any $2$-end-coloring, where $J_f^*(v)$ is the union of all odd integers smaller than $f(v)$ and the integer $f(v)$ itself. This is a generalization of the $(1,f)$-odd factor characterization theorem, and answers a problem of Cui and Kano. We also derive an analogous characterization for graphs of odd orders, which addresses a problem of Akiyama and Kano.

Author

Lu, Hongliang; Wang, David G. L.

Published

2015

Language

EN