# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2019: 0.755

SCImago Journal Rank (SJR) 2019: 0.600

Rejection Rate (2018-2019): c. 84%

# Discussiones Mathematicae Graph Theory

Article in press

Authors:

S. Nakamura

Title:

Distribution of contractible edges and the structure of noncontractible edges having endvertices with large degree in a 4-connected graph

Source:

Discussiones Mathematicae Graph Theory

Received: 2018-03-20, Revised: 2019-02-04, Accepted: 2019-05-06, https://doi.org/10.7151/dmgt.2229

Abstract:

Let $G$ be a 4-connected graph $G$, and let $E_c(G)$ denote the set of 4-contractible edges of $G$. We prove results concerning the distribution of edges in $E_c(G)$. Roughly speaking, we show that there exists a set $\mathcal{K}_0$ and a mapping $\varphi: \mathcal{K}_0 \to E_c(G)$ such that $|\varphi^{-1}(e)| \le 4$ for each $e \in E_c(G)$.

Keywords:

4-connected graph, contractible edge, cross free