Section: New Results

Strong chromatic index of planar graphs with large girth

Let $\Delta$ be an integer. In [18] , we prove that every planar graph with maximum degree $\Delta$ and girth at least $10\Delta +46$ is strong $(2\Delta -1)$-edge-colorable, that is best possible (in terms of number of colors) as soon as $G$ contains two adjacent vertices of degree $\Delta$. This improves the best previous result when $\Delta \ge 6$.