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» Coloring powers of planar graphs
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EJC
2008
13 years 7 months ago
Coloring 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. ...
Zdenek Dvorak, Daniel Král, Pavel Nejedl&ya...
DAM
2006
124views more  DAM 2006»
13 years 7 months ago
Coloring copoints of a planar point set
To a set of n points in the plane, one can associate a graph that has less than n2 vertices and has the property that k-cliques in the graph correspond vertex sets of convex k-gon...
Walter Morris
ISAAC
2004
Springer
141views Algorithms» more  ISAAC 2004»
14 years 1 months ago
Weighted Coloring on Planar, Bipartite and Split Graphs: Complexity and Improved Approximation
We study complexity and approximation of min weighted node coloring in planar, bipartite and split graphs. We show that this problem is NP-complete in planar graphs, even if they a...
Jérôme Monnot, Vangelis Th. Paschos, ...
ALGORITHMICA
2006
138views more  ALGORITHMICA 2006»
13 years 7 months ago
Planar Graph Coloring Avoiding Monochromatic Subgraphs: Trees and Paths Make It Difficult
We consider the problem of coloring a planar graph with the minimum number of colors so that each color class avoids one or more forbidden graphs as subgraphs. We perform a detail...
Hajo Broersma, Fedor V. Fomin, Jan Kratochví...
JCT
2007
77views more  JCT 2007»
13 years 7 months ago
Exponentially many 5-list-colorings of planar graphs
We prove that every planar graph with n vertices has at least 2n/9 distinct list-colorings provided every vertex has at least five available colors. © 2006 Elsevier Inc. All rig...
Carsten Thomassen