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DM
2010
131views more  DM 2010»
13 years 7 months ago
Planar graphs without adjacent cycles of length at most seven are 3-colorable
We prove that every planar graph in which no i-cycle is adjacent to a j-cycle whenever 3 i j 7 is 3-colorable and pose some related problems on the 3-colorability of planar grap...
Oleg V. Borodin, Mickaël Montassier, Andr&eac...
COLOGNETWENTE
2009
13 years 8 months ago
Colored Trees in Edge-Colored Graphs
We consider maximum properly edge-colored trees in edge-colored graphs Gc . We also consider the problem where, given a vertex r, determine whether the graph has a spanning tree r...
A. Abouelaoualim, V. Borozan, Yannis Manoussakis, ...
JCT
2010
111views more  JCT 2010»
13 years 5 months ago
Anti-Ramsey properties of random graphs
We call a coloring of the edge set of a graph G a b-bounded coloring if no color is used more than b times. We say that a subset of the edges of G is rainbow if each edge is of a ...
Tom Bohman, Alan M. Frieze, Oleg Pikhurko, Cliffor...
DAM
2011
13 years 2 months ago
On the b-coloring of P4-tidy graphs
A b-coloring of a graph is a coloring such that every color class admits a vertex adjacent to at least one vertex receiving each of the colors not assigned to it. The b-chromatic ...
Clara Inés Betancur Velasquez, Flavia Bonom...
MST
2010
98views more  MST 2010»
13 years 5 months ago
Why Almost All k-Colorable Graphs Are Easy to Color
Coloring a k-colorable graph using k colors (k ≥ 3) is a notoriously hard problem. Considering average case analysis allows for better results. In this work we consider the unif...
Amin Coja-Oghlan, Michael Krivelevich, Dan Vilench...