论文信息 - Planar graphs without 5- and 7-cycles and without adjacent triangles are 3-colorable

Planar graphs without 5- and 7-cycles and without adjacent triangles are 3-colorable

It is known that planar graphs without cycles of length from 4 to 7 are 3-colorable [O.V. Borodin, A.N. Glebov, A. Raspaud, M.R. Salavatipour, Planar graphs without cycles of length from 4 to 7 are 3-colorable, J. Combin. Theory Ser. B 93 (2005) 303-311]. We improve this result by proving that every planar graph without 5- and 7-cycles and without adjacent triangles is 3-colorable. Also, we give counterexamples to the proof of the same result in [B. Xu, On 3-colorable plane graphs without 5- and 7-cycles, J. Combin. Theory Ser. B 96 (2006) 958-963].

André Raspaud | Mickaël Montassier | Alexei N. Glebov | Oleg V. Borodin

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