Light edges in 1‐planar graphs

descriptionPublicationkeyboard_double_arrow_right Article 20 Jun 2022 English Publisher:WileyJournal:Journal of Graph Theory, volume 101, pages 746-768 (issn: 0364-9024, eissn: 1097-0118,

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Authors: Juan Liu; Yiqiao Wang; Weifan Wang;

doi: 10.1002/jgt.22851

Light edges in 1‐planar graphs

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Abstract

AbstractA graph is 1‐planar if it can be drawn in the plane so that each edge is crossed by at most one other edge. In this paper, we prove that every 1‐planar graph with minimum degree at least 3 contains an edge with such that one of the following holds: (1) and ; (2) and ; (3) and ; (4) and ; (5) . The upper bound on in each of the five items except the second is sharp.

Related Organizations

University of Science and Technology of China
China (People's Republic of)
Beijing University of Chinese Medicine
China (People's Republic of)
Zhejiang Normal University
China (People's Republic of)

Keywords

Extremal problems in graph theory, associated plane graph, Vertex degrees, 1-planar graph, light edge, Planar graphs; geometric and topological aspects of graph theory, minimum degree

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