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On doubly light triangles in plane graphs. (English) Zbl 1277.05047
Summary: We prove that each 3-connected plane graph of minimum degree 5 contains a triangular face of the weight at most 17 such that the sum of sizes of three its adjacent faces is at most 13. This extends theorem of Borodin on light triangles in normal plane maps. In addition, we present several related results concerning configurations of faces around a triangle in various families of plane graphs.

##### MSC:
 05C10 Planar graphs; geometric and topological aspects of graph theory
##### Keywords:
plane graph; light graph; triangle
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##### References:
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