Note: coloring the square of a K4-minor free graph

Authors:
Ko-Wei Lih;Wei-Fan Wang;Xuding Zhu
Affiliations:
Institute of Mathematics, Academia Sinica, Nankang, Taipei 115, Taiwan;Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China;Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Taiwan
Venue:
Discrete Mathematics
Year:
2003

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Abstract

Let G be a K4-minor free graph with maximum degree Δ. We prove that the chromatic number of the square of G is at most (i) Δ + 3 if 2 ≤ Δ ≤ 3; or (ii) [3Δ/2] + 1 if Δ ≥ 4. Examples are given to show the bounds can be attained.