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Petersen-colorings and some families of snarks. (English) Zbl 1301.05124

Summary: In this paper we study Petersen-colorings and strong Petersen-colorings on some well known families of snarks, e.g. Blanuša snarks, Goldberg snarks and flower snarks. In particular, it is shown that flower snarks have a Petersen-coloring but they do not have a strong Petersen-coloring. Furthermore it is proved that possible minimum counterexamples to Jaeger’s Petersen-coloring conjecture [F. Jaeger, in: Selected topics in graph theory, Vol. 3, 71–95 (1988; Zbl 0658.05034)] do not contain a specific subdivision of \( K_{3,3}\).

MSC:

05C15 Coloring of graphs and hypergraphs
05C21 Flows in graphs
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)

Citations:

Zbl 0658.05034
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