Informace o publikaci

Coloring even-faced graphs in the torus and the Klein bottle



Rok publikování 2008
Druh Článek v odborném periodiku
Časopis / Zdroj Combinatorica : an international journal of the János Bolyai Mathematical Society
Popis We prove that a triangle-free graph drawn in the torus with all faces bounded by even walks is 3-colorable if and only if it has no subgraph isomorphic to the Cayley graph C (Z(13); 1, 5). We also prove that a non-bipartite quadrangulation of the Klein bottle is 3-colorable if and only if it has no non-contractible separating cycle of length at most four and no odd walk homotopic to a non-contractible two-sided simple closed curve. These results settle a conjecture of Thomassen and two conjectures of Archdeacon, Hutchinson, Nakamoto, Negami and Ota.

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