Injective choosability of planar graphs of girth five and six
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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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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It is proved that a planar graph G without five cycles is three degenerate, hence, four choosable, and it is also edge-(A( G) + l)h c oosable. @ 2002 Elsevier Science Ltd. All rights reserved. Keywords-Choosability, Edge choosability, Degeneracy, Planar graph.
متن کاملColoring squares of planar graphs with girth six
Wang and Lih conjectured that for every g ≥ 5, there exists a number M(g) such that the square of a planar graph G of girth at least g and maximum degree ∆ ≥ M(g) is (∆+1)-colorable. The conjecture is known to be true for g ≥ 7 but false for g ∈ {5, 6}. We show that the conjecture for g = 6 is off by just one, i.e., the square of a planar graph G of girth at least six and sufficiently large max...
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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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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2012
ISSN: 0012-365X
DOI: 10.1016/j.disc.2011.10.029