Joins of 1-Planar Graphs

被引：6

作者：

Czap, Julius ^{[1
]}

Hudak, David ^{[2
]}

Madaras, Tomas ^{[3
]}

机构：

[1] Tech Univ Kosice, Fac Econ, Dept Appl Math & Business Informat, Kosice 04001, Slovakia

[2] VSL Software As, Kosice 04001, Slovakia

[3] Pavol Jozef Safarik Univ, Fac Sci, Inst Math, Kosice 04001, Slovakia

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2014年 / 30卷 / 11期

关键词：

1-Planar graph; join product;

D O I：

10.1007/s10114-014-4017-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A graph is called 1-planar if it admits a drawing in the plane such that each edge is crossed at most once. In this paper, we study 1-planar graph joins. We prove that the join G + H is 1-planar if and only if the pair [G, H] is subgraph-majorized by one of pairs [C-3 boolean OR C-3, C-3], [C-4, C-4], [C-4, C-3], [K-2,K-1,K-1, P-3] in the case when both elements of the graph join have at least three vertices. If one element has at most two vertices, then we give several necessary/sufficient conditions for the bigger element.

引用

页码：1867 / 1876

页数：10

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