期刊
AIMS MATHEMATICS
卷 8, 期 7, 页码 17081-17090出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/math.2023872
关键词
injective coloring; planar graph; cycle
This paper proves that for a planar graph G with g(G) >= 5, Delta(G) >= 20, and without adjacent 5-cycles, the injective chromatic number chi i(G) is less than or equal to Delta(G) + 2.
A k-injective-coloring of a graph G is a mapping c : V (G) -> [1, 2, center dot center dot center dot , k} such that c (u) # c (v) for any two vertices u and v if u and v have a common vertex. The injective chromatic number of G, denoted by chi i (G), is the least k such that G has an injective k-coloring. In this paper, we prove that for planar graph G with g (G) >= 5, Delta (G) >= 20 and without adjacent 5-cycles, chi i (G) <= Delta (G) + 2.
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