5-choosability of graphs with crossings far apart
نویسندگان
چکیده
منابع مشابه
5-choosability of Graphs with Crossings Far Apart
We give a new proof of the fact that every planar graph is 5choosable, and use it to show that every graph drawn in the plane so that the distance between every pair of crossings is at least 15 is 5-choosable. At the same time we may allow some vertices to have lists of size four only, as long as they are far apart and far from the crossings. Thomassen [5] gave a strikingly beautiful proof that...
متن کامل5-choosability of graphs with 2 crossings
We show that every graph with two crossings is 5-choosable. We also prove that every graph which can be made planar by removing one edge is 5-choosable. Key-words: list colouring, choosability, crossing number † Universidade Federal do Ceará, Departamento de Computaçao, Bloco 910, Campus do Pici, Fortaleza, Ceará, CEP 60455-760, Brasil. [email protected]; Partially supported by CNPq/Brazil. ‡ P...
متن کامل3-choosability of Planar Graphs with ( 4)-cycles Far Apart
A graph is k-choosable if it can be colored whenever every vertex has a list of at least k available colors. We prove that if cycles of length at most four in a planar graph G are pairwise far apart, then G is 3-choosable. This is analogous to the problem of Havel regarding 3-colorability of planar graphs with triangles far apart.
متن کاملColoring planar graphs with triangles far apart
We settle a problem of Havel by showing that there exists an absolute constant d such that if G is a planar graph in which every two distinct triangles are at distance at least d, then G is 3-colorable.
متن کاملGraphs with Two Crossings Are 5-Choosable
A graph G is k-choosable if G can be properly colored whenever every vertex has a list of at least k available colors. Thomassen’s theorem states that every planar graph is 5-choosable. We extend the result by showing that every graph with at most two crossings is 5-choosable.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2017
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2016.11.004