We give nontrivial bounds for the inductiveness or degeneracy of power graphs Gk of a planar graph G. This implies bounds for the chromatic number as well, since the inductiveness ...
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 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...