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Cosupereulerian graphs
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Title: Cosupereulerian graphs Abstract: A subset $S$ of a matroid $M$ is eulerian if $S$ is a disjoint union of circuits. A matroid with an eulerian subset spanning in $M$ is supereulerian, and a connected graph $G$ is supereulerian if its cycle matroid $M(G)$ is supereulerian. A graph $G$ is cosupereulerian if its cocycle matroid $M^*(G)$ is supereulerian. In [J. of Graph Theory, 664 (2010), 1-11], it is proved that every 3-edge-connected graph with circumference at most 8 is supereulerian. This result can be improved to the form that every 3-edge-connected graph |
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