We show efficient algorithms for edge-coloring planar graphs. Our main result is a linear-time algorithm for coloring planar graphs with maximum degree with max{, 9} colors. Thus...
A proper vertex coloring of a graph is equitable if the sizes of its color classes differ by at most one. In this note, we prove that if G is a graph such that for each edge xy E...
A b-coloring is a coloring of the vertices of a graph such that each color class contains a vertex that has a neighbor in all other color classes, and the b-chromatic number of a ...
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...
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, ...