On Choosability with Separation of Planar Graphs with Forbidden Cycles
نویسندگان
چکیده
منابع مشابه
On Choosability with Separation of Planar Graphs with Forbidden Cycles
We study choosability with separation which is a constrained version of list coloring of graphs. A (k, d)-list assignment L of a graph G is a function that assigns to each vertex v a list L(v) of at least k colors and for any adjacent pair xy, the lists L(x) and L(y) share at most d colors. A graph G is (k, d)-choosable if there exists an L-coloring of G for every (k, d)-list assignment L. This...
متن کامل(4, 2)-Choosability of Planar Graphs with Forbidden Structures
All planar graphs are 4-colorable and 5-choosable, while some planar graphs are not 4-choosable. Determining which properties guarantee that a planar graph can be colored using lists of size four has received significant attention. In terms of constraining the structure of the graph, for any l∈{3,4,5,6,7}" role="presentation" style="box-sizing: border-box; display: inline; line-height: normal; ...
متن کاملAdaptable choosability of planar graphs with sparse short cycles
Given a (possibly improper) edge-colouring F of a graph G, a vertex colouring of G is adapted to F if no colour appears at the same time on an edge and on its two endpoints. A graph G is called adaptably k-choosable (for some positive integer k) if for any list assignment L to the vertices of G, with |L(v)| ≥ k for all v, and any edge-colouring F of G, G admits a colouring c adapted to F where ...
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 کاملChoosability and edge choosability of planar graphs without five cycles
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2015
ISSN: 0364-9024
DOI: 10.1002/jgt.21875