Joins of 1-planar graphs |
| |
| Authors: | Július Czap Dávid Hudák Tomáš Madaras |
| |
| Institution: | [1]Department of Applied Mathematics and Business Informatics, Faculty of Economics Technical University of Kosice, Nemcovej32, 040 01 Kosice, Slovakia; [2]VSL Software, a.s., Lomend 8, 04001 Kogice, Slovakia; [3]Institute of Mathematics, Faculty of Science, Pavol Jozef Safdrik University Jesennd 5, 040 01 Kogice, Slovakia |
| |
| Abstract: | 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 ∪ C 3, C 3], C 4, C 4], C 4,C 3], K 2,1,1, 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. |
| |
| Keywords: | 1-Planar graph join product |
| 本文献已被 CNKI 维普 SpringerLink 等数据库收录！ |
|
