The Matching Extendability of Optimal 1-Planar Graphs

被引：9
|
作者：
Fujisawa, Jun [1 ]
Segawa, Keita [2 ]
Suzuki, Yusuke [3 ]
机构：
[1] Keio Univ, Fac Business & Commerce, Kohoku Ku, Hiyoshi 4-1-1, Yokohama, Kanagawa 2238521, Japan
[2] Niigata Univ, Grad Sch Sci & Technol, Nishi Ku, 8050 Ikarashi 2 No Cho, Niigata 9502181, Japan
[3] Niigata Univ, Dept Math, Nishi Ku, 8050 Ikarashi 2 No Cho, Niigata 9502181, Japan
来源：
GRAPHS AND COMBINATORICS | 2018年 / 34卷 / 05期
基金：
日本学术振兴会;
关键词：
Optimal 1-planar graph; Perfect matching; Extendability; PLANAR GRAPHS;
D O I：
10.1007/s00373-018-1932-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A graph G is said to be 1-planar if it can be drawn on the sphere or plane so that any edge of G has at most one crossing point with another edge. Moreover, G is called an optimal 1-planar graph if vertical bar E(G)vertical bar = 4 vertical bar V(G)vertical bar - 8. In this paper, we investigate the matching extendability of optimal 1-planar graphs. It is shown that every optimal 1-planar graph G of even order is 2-extendable unless G contains a 4-cycle C which separates the graph into two odd components. Moreover, for any 5-connected optimal 1-planar graph, we characterize a matching with three edges which is not extendable.
引用
收藏
页码：1089 / 1099
页数：11
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