Acyclic 3-choosability of sparse graphs with girth at least 7
نویسندگان
چکیده
منابع مشابه
Sparse graphs of girth at least five are packable
A graph is packable if it is a subgraph of its complement. The following statement was conjectured by Faudree, Rousseau, Schelp and Schuster in 1981: every non-star graph G with girth at least 5 is packable. The conjecture was proved by Faudree et al. with the additional condition that G has at most 5n − 2 edges. In this paper, for each integer k ≥ 3, we prove that every non-star graphwith girt...
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Let G be a plane graph of girth at least 4. Two cycles of G are intersecting if they have at least one vertex in common. In this paper, we show that if a plane graph G has neither intersecting 4-cycles nor a 5-cycle intersecting with any 4-cycle, then G is 3-choosable, which extends one of Thomassen’s results [C. Thomassen, 3-list-coloring planar graphs of girth 5, J. Combin. Theory Ser. B 64 (...
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We consider improper colorings (sometimes called generalized, defective or relaxed colorings) in which every color class has a bounded degree. We propose a natural extension of improper colorings: acyclic improper choosability. We prove that subcubic graphs are acyclically (3,1)∗-choosable (i.e. they are acyclically 3-choosable with color classes of maximum degree one). Using a linear time algo...
متن کاملChoosability of planar graphs of girth 5
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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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2010
ISSN: 0012-365X
DOI: 10.1016/j.disc.2010.05.032