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arXiv · 1802.07991

Decomposition of a graph into two disjoint odd subgraphs

Mikio Kano·Gyula Y. Katona·Kitti Varga
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Abstract

An odd (resp. even) subgraph in a multigraph is its subgraph in which every vertex has odd (resp. even) degree. We say that a multigraph can be decomposed into two odd subgraphs if its edge set can be partitioned into two sets so that both form odd subgraphs. In this paper we give a necessary and sufficient condition for the decomposability of a multigraph into two odd subgraphs. We also present a polynomial time algorithm for finding such a decomposition or showing its non-existence. We also deal with the case of the decomposability into an even subgraph and an odd subgraph.

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Mikio Kano, Gyula Y. Katona, Kitti Varga. 2018-02-22. Decomposition of a graph into two disjoint odd subgraphs. https://doi.org/10.7151/dmgt.2372

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