A smaller planar graph without 4-, 5-cycles and intersecting triangles that is not 3-choosable

Authors:
De-Qiang Wang;Yu-Peng Wen;Ke-Lun Wang
Affiliations:
Institute of Nautical Science and Technology, Dalian Maritime University, Dalian 116026, China and Mathematics Department, Dalian Maritime University, Dalian 116026, China;School of Science, Jilin Institute of Chemical, Jilin 132022, China;Mathematics Department, Dalian Maritime University, Dalian 116026, China
Venue:
Information Processing Letters
Year:
2008

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Discrete Mathematics
A not 3-choosable planar graph without 3-cycles

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Abstract

In 2006, Montassier et al. constructed a planar graph without 4-, 5-cycles and intersecting triangles that is not 3-choosable [M. Montassier, A. Raspaud, W. Wang, Bordeaux 3-color conjecture and 3-choosability, Discrete Math. 306 (2006) 573-579]. It has 506 vertices. In this paper, we construct a smaller planar graph with the same properties. The planar graph has 380 vertices.