Three-regular Subgraphs of Four-regular Graphs'

@article{Moreno1998ThreeregularSO,
  title={Three-regular Subgraphs of Four-regular Graphs'},
  author={Oscar Moreno and Victor Zinoviev},
  journal={Eur. J. Comb.},
  year={1998},
  volume={19},
  pages={369-373}
}
The Berge–Sauer conjecture (see [2, 3]) says that any simple (no multiple edges and loops) 4-regular graph contains a 3-regular subgraph. This conjecture was proved in [4, 6]. In [1, 2] the Chevalley–Warning theorem was used to extend this result to graphs with multiple edges, which are 4-regular plus an edge. Our main result, Theorem 2.2, presents the sufficient condition for a 4-regular graph with multiple edges to have a 3-regular subgraph. It gives the new 4-regular graphs with multiple… CONTINUE READING

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