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Weight of light chords 4-cycles in IC-planar graphs with degree restrictions. (Chinese. English summary) Zbl 1474.05107

Summary: The graph formed by removing an edge from a complete graph \({k_4}\) was called chordal 4-cycle. By discharging method, the author discussed the weight of 4-cycle with chords in IC-planar graphs with degree restrictions. The author proved that each IC-planar graph with minimum vertex degree at least 5 and minimum edge degree at least 11 contained a light chordal 4-cycle \({v_1}{v_2}{v_3}{v_4}{v_1}\), and proved that the upper bound of weight of this kind of light chordal 4-cycle was at most 37.

MSC:

05C10 Planar graphs; geometric and topological aspects of graph theory
05C38 Paths and cycles
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