On graphs double-critical with respect to the colouring number - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2015

On graphs double-critical with respect to the colouring number

Abstract

The colouring number col($G$) of a graph $G$ is the smallest integer $k$ for which there is an ordering of the vertices of $G$ such that when removing the vertices of $G$ in the specified order no vertex of degree more than $k-1$ in the remaining graph is removed at any step. An edge $e$ of a graph $G$ is said to be double-col-critical if the colouring number of $G-V(e)$ is at most the colouring number of $G$ minus 2. A connected graph G is said to be double-col-critical if each edge of $G$ is double-col-critical. We characterise the double-col-critical graphs with colouring number at most 5. In addition, we prove that every 4-col-critical non-complete graph has at most half of its edges being double-col-critical, and that the extremal graphs are precisely the odd wheels on at least six vertices. We observe that for any integer $k$ greater than 4 and any positive number $ε$, there is a $k$-col-critical graph with the ratio of double-col-critical edges between $1- ε$ and 1.
Fichier principal
Vignette du fichier
2320-9766-1-PB.pdf (310.02 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01349043 , version 1 (26-07-2016)

Identifiers

Cite

Matthias Kriesell, Anders Pedersen. On graphs double-critical with respect to the colouring number. Discrete Mathematics and Theoretical Computer Science, 2015, Vol. 17 no.2 (2), pp.49-62. ⟨10.46298/dmtcs.2129⟩. ⟨hal-01349043⟩

Collections

TDS-MACS
47 View
975 Download

Altmetric

Share

Gmail Facebook X LinkedIn More