Decomposition of a graph into two disjoint odd subgraphs
Combinatorics
2022-09-02 v1
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.
Keywords
Cite
@article{arxiv.1802.07991,
title = {Decomposition of a graph into two disjoint odd subgraphs},
author = {Mikio Kano and Gyula Y. Katona and Kitti Varga},
journal= {arXiv preprint arXiv:1802.07991},
year = {2022}
}