Planar graphs without 4- and 6-cycles are (7: 2)-colorable

Haitao Wu, Yaojun Chen and Xiaolan Hu ()
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Haitao Wu: Nanjing University
Yaojun Chen: Nanjing University
Xiaolan Hu: Central China Normal University

Journal of Combinatorial Optimization, 2020, vol. 40, issue 1, No 4, 45-58

Abstract: Abstract Let $$G=(V(G),E(G))$$G=(V(G),E(G)) be a graph and s, t integers with $$s\le t$$s≤t. If we can assign an s-subset $$\phi (v)$$ϕ(v) of the set $$\{1, 2,\ldots ,t\}$${1,2,…,t} to each vertex v of V(G) such that $$\phi (u)\cap \phi (v)=\emptyset $$ϕ(u)∩ϕ(v)=∅ for every edge $$uv\in E(G)$$uv∈E(G), then G is called (t : s)-colorable, and such an assignment $$\phi $$ϕ is called a (t : s)-coloring of G. Let $$C_n$$Cn denote a cycle of length n. In this paper, we show that every planar graph without $$C_4$$C4 and $$C_6$$C6 is (7 : 2)-colorable and thus has fractional chromatic number at most 7/2.

Keywords: Planar graphs; Cycles; Fractional coloring (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10878-020-00571-7

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