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Light Edges in 3-Connected 2-Planar Graphs With Prescribed Minimum Degree

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Abstract

A graph is called 2-planar if it can be drawn in the plane such that each edge is crossed by at most other two edges. The weight of an edge is the sum of degrees of its ends. In the present paper, we focus on 3-connected 2-planar graphs with minimum degree 6 and show the existence of edges with weight at most 30 by a discharging process.

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Authors and Affiliations

  1. Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin, 300071, China

    Zai Ping Lu & Ning Song

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  1. Zai Ping Lu
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  2. Ning Song
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Correspondence to Ning Song.

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Communicated by Xueliang Li.

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Lu, Z.P., Song, N. Light Edges in 3-Connected 2-Planar Graphs With Prescribed Minimum Degree. Bull. Malays. Math. Sci. Soc. 41, 1265–1274 (2018). https://doi.org/10.1007/s40840-016-0389-0

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  • DOI: https://doi.org/10.1007/s40840-016-0389-0

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