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Cycle decompositions of pathwidth-6 graphs
[article]
2017
arXiv
pre-print
Haj\'os conjecture asserts that a simple Eulerian graph on n vertices can be decomposed into at most (n - 1)/2 cycles. The conjecture is only proved for graph classes in which every element contains vertices of degree 2 or 4. We develop new techniques to construct cycle decompositions. They work on the common neighbourhood of two degree-6 vertices. With these techniques we find structures that cannot occur in a minimal counterexample to Haj\'os conjecture and verify the conjecture for Eulerian
arXiv:1705.07066v2
fatcat:knxu5gn42belra4zows4psl6qm