Coloring even-faced graphs in the torus and the Klein bottle
نویسندگان
چکیده
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(Z13;1,5). We also prove that a non-bipartite quadrangulation of the Klein bottle is 3colorable 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.
منابع مشابه
On the restricted matching extension of graphs on the torus and the Klein bottle
Aldred and Plummer proved that every 6-connected even graph minimally embedded on the torus or the Klein bottle is E(1, n)(n ≤ 3) and E(0, n)(n ≤ 5) [R.E.L. Aldred, M.D. Plummer, Restricted matching in graphs of small genus, Discrete Math. 308 (2008) 5907–5921]. In this paper, we can remove the upper bounds on n by showing that every even 6-regular graph G embedded on the torus or the Klein bot...
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ورودعنوان ژورنال:
- Combinatorica
دوره 28 شماره
صفحات -
تاریخ انتشار 2008