Injective choosability of subcubic planar graphs with girth 6
نویسندگان
چکیده
منابع مشابه
Injective choosability of subcubic planar graphs with girth 6
An injective coloring of a graph G is an assignment of colors to the vertices of G so that any two vertices with a common neighbor have distinct colors. A graph G is injectively k-choosable if for any list assignment L, where |L(v)| ≥ k for all v ∈ V (G), G has an injective L-coloring. Injective colorings have applications in the theory of error-correcting codes and are closely related to other...
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We first show that the choose number of the square of a subcubic graph with maximum average degree less than 18/7 is at most 6. As a corollary, we get that the choose number of the square of a planar graph with girth at least 9 is at most 6. We then show that the choose number of the square of a subcubic planar graph with girth at least 13 is at most 5. Key-words: colouring, list colouring, pla...
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Thomassen proved that any plane graph of girth 5 is list-colorable from any list assignment such that all vertices have lists of size two or three and the vertices with list of size two are all incident with the outer face and form an independent set. We present a strengthening of this result, relaxing the constraint on the vertices with list of size two. This result is used to bound the size o...
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The trivial lower bound for the 2-distance chromatic number χ2(G) of any graph G with maximum degree ∆ is ∆+1. It is known that χ2 = ∆+1 if the girth g of G is at least 7 and ∆ is large enough. There are graphs with arbitrarily large ∆ and g ≤ 6 having χ2(G) ≥ ∆ + 2. We prove the 2-distance 4-colorability of planar subcubic graphs with g ≥ 22.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2017
ISSN: 0012-365X
DOI: 10.1016/j.disc.2017.05.014