On 3-coloring of plane graphs without adjacent short cycles
Yingqian Wang · Journal of Zhejiang Normal University · 2009
It was studied 3-colorability of plane graphs by the method of identifying vertices.Some structural properties were explored of the minimal counterexamples of plane graphs without adjacent short cycles,the outer cycle of which had a partial 3-coloring not being extended to the whole graph.As a result,it was proved that plane graphs without adjacent 8——cycles were 3-colorable.The result and method would be useful for studying Steinberg′s conjecture and Havel′s problem.