Cycle decompositions of pathwidth-6 graphs [article]

Elke Fuchs, Laura Gellert, Irene Heinrich
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
more » ... raphs of pathwidth at most 6. This implies that these graphs satisfy the small cycle double cover conjecture.
arXiv:1705.07066v2 fatcat:knxu5gn42belra4zows4psl6qm