Constructing a Family of 4-Critical Planar Graphs with High Edge-Density
A graph $G=(V,E)$ is a $k$-critical graph if $G$ is not $(k -1)$-colorable but $G-e$ is $(k-1)$-colorable for every $e\in E(G)$. In this paper, we construct a family of 4-critical planar graphs with $n$ vertices and $\frac{7n-13}{3}$ edges. As a consequence, this improved the bound for the maximum e...
Saved in:
Main Authors | , |
---|---|
Format | Journal Article |
Language | English |
Published |
02.09.2015
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | A graph $G=(V,E)$ is a $k$-critical graph if $G$ is not $(k -1)$-colorable
but $G-e$ is $(k-1)$-colorable for every $e\in E(G)$. In this paper, we
construct a family of 4-critical planar graphs with $n$ vertices and
$\frac{7n-13}{3}$ edges. As a consequence, this improved the bound for the
maximum edge density obtained by Abbott and Zhou. We conjecture that this is
the largest edge density for a 4-critical planar graph. |
---|---|
DOI: | 10.48550/arxiv.1509.00760 |