Injective Colorings of Graphs with Low Average Degree
نویسندگان
چکیده
منابع مشابه
Injective colorings of sparse graphs
Let mad(G) denote the maximum average degree (over all subgraphs) of G and let χi(G) denote the injective chromatic number of G. We prove that if mad(G) ≤ 5 2 , then χi(G) ≤ ∆(G) + 1; and if mad(G) < 42 19 , then χi(G) = ∆(G). Suppose that G is a planar graph with girth g(G) and ∆(G) ≥ 4. We prove that if g(G) ≥ 9, then χi(G) ≤ ∆(G) + 1; similarly, if g(G) ≥ 13, then χi(G) = ∆(G).
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ژورنال
عنوان ژورنال: Algorithmica
سال: 2010
ISSN: 0178-4617,1432-0541
DOI: 10.1007/s00453-010-9425-x