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Parity Subgraphs with Few Common Edges and Nowhere-Zero 5-Flow

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Abstract

A parity subgraph of a graph is a spanning subgraph such that the degrees of all vertices have the same parity in both the subgraph and the original graph. Let \(G\) be a cyclically 6-edge-connected cubic graph. Steffen (Intersecting 1-factors and nowhere-zero 5-flows 1306.5645, 2013) proved that \(G\) has a nowhere-zero 5-flow if \(G\) has two perfect matchings with at most two intersections. In this paper, we show that \(G\) has a nowhere-zero 5-flow if \(G\) has two parity subgraphs with at most two common edges, which generalizes Steffen’s result.

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Authors and Affiliations

  1. School of Mathematical Sciences, Wu Wen-Tsun Key Laboratory of Mathematics, University of Science and Technology of China, Hefei, 230026, Anhui, China

    Jiaao Li, Xinmin Hou, Zhen-Mu Hong & Xiaofeng Ding

Authors
  1. Jiaao Li
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  2. Xinmin Hou
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  3. Zhen-Mu Hong
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  4. Xiaofeng Ding
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Corresponding author

Correspondence to Xinmin Hou.

Additional information

The work was supported by the NNSF of China (No. 11271348) and the Fundamental Research Funds for the Central Universities.

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Li, J., Hou, X., Hong, ZM. et al. Parity Subgraphs with Few Common Edges and Nowhere-Zero 5-Flow. Graphs and Combinatorics 31, 1555–1566 (2015). https://doi.org/10.1007/s00373-014-1464-7

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  • DOI: https://doi.org/10.1007/s00373-014-1464-7

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