Tian, Jingjing Weight of light chords 4-cycles in IC-planar graphs with degree restrictions. (Chinese. English summary) Zbl 1474.05107 J. Jilin Univ., Sci. 58, No. 5, 1093-1099 (2020). 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 Keywords:IC-planar graph; discharging method; weight; chordal 4-cycle PDFBibTeX XMLCite \textit{J. Tian}, J. Jilin Univ., Sci. 58, No. 5, 1093--1099 (2020; Zbl 1474.05107) Full Text: DOI