Bibliographic Details
| Title: |
ON THE SIZE OF MATCHINGS IN 1-PLANAR GRAPH WITH HIGH MINIMUM DEGREE. |
| Authors: |
YUANQIU HUANG, ZHANGDONG OUYANG, FENGMING DONG |
| Superior Title: |
SIAM Journal on Discrete Mathematics; 2022, Vol. 36 Issue 4, p2570-2584, 15p |
| Subject Terms: |
PLANAR graphs, GRAPH theory, LOGICAL prediction |
| Abstract: |
A matching of a graph is a set of edges without common end vertex. A graph is called 1-planar if it admits a drawing in the plane such that each edge is crossed at most once. Recently, Biedl and Wittnebel [J. Graph Theory, 99 (2022), pp. 217--230] proved that every 1-planar graph with minimum degree 3 and n \geq 7 vertices has a matching of size at least n+12 7, which is tight for some graphs. They also provided tight lower bounds for the sizes of matchings in 1-planar graphs with minimum degree 4 or 5. In this paper, we show that any 1-planar graph with minimum degree 6 and n \geq 36 vertices has a matching of size at least 3n+4 7, and this lower bound is tight. Our result confirms a conjecture posed by Biedl and Wittnebel [J. Graph Theory, 99 (2022), pp. 217--230]. [ABSTRACT FROM AUTHOR] |
|
Copyright of SIAM Journal on Discrete Mathematics is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) |
| Database: |
Complementary Index |
