Cycle decompositions of pathwidth‐6 graphs
Copyright policy )Cycle decompositions of pathwidth‐6 graphs
AbstractHajós' conjecture asserts that a simple Eulerian graph on vertices can be decomposed into at most 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 neighborhood of two degree‐6 vertices. With these techniques, we find structures that cannot occur in a minimal counterexample to Hajós' conjecture and verify the conjecture for Eulerian graphs of pathwidth at most 6. This implies that these graphs satisfy the small cycle double cover conjecture.
ddc:510, Eulerscher Graph, Eulerian and Hamiltonian graphs, decomposition, Eulerian graph theory, Schaltzeichen, 510, Decomposition (Mathematics), 05C38, 05C45, Hajós conjecture, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), FOS: Mathematics, Mathematics - Combinatorics, cycle decomposition, Combinatorics (math.CO), Zerlegung, Mathematik, Eulerian graphs, Paths and cycles, circuit, info:eu-repo/classification/ddc/500, ddc: ddc:510
ddc:510, Eulerscher Graph, Eulerian and Hamiltonian graphs, decomposition, Eulerian graph theory, Schaltzeichen, 510, Decomposition (Mathematics), 05C38, 05C45, Hajós conjecture, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), FOS: Mathematics, Mathematics - Combinatorics, cycle decomposition, Combinatorics (math.CO), Zerlegung, Mathematik, Eulerian graphs, Paths and cycles, circuit, info:eu-repo/classification/ddc/500, ddc: ddc:510
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