English

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}
}
R2 v1 2026-06-23T00:29:55.837Z