Back to Search
Start Over
A new note on 1-planar graphs with minimum degree 7.
- Source :
-
Discrete Applied Mathematics . May2024, Vol. 348, p165-183. 19p. - Publication Year :
- 2024
-
Abstract
- A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once. It is well-known that each 1-planar graph has its minimum degree at most 7. Recently, Biedl (2021) showed that any 1-planar graph with minimum degree 7 has at least 24 vertices. In this paper, we characterize 1-planar graphs with 24 vertices and minimum degree 7. Furthermore, we prove that any 1-planar graph of odd order with minimum degree 7 has at least 29 vertices, and the lower bound is tight. In addition, we also characterize 5-connected 7-regular maximal 1-plane graphs. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0166218X
- Volume :
- 348
- Database :
- Academic Search Index
- Journal :
- Discrete Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 176008104
- Full Text :
- https://doi.org/10.1016/j.dam.2024.01.026