Improved lower bounds on the number of edges in list critical and online list critical graphs

Henry Kierstead, Landon Rabern

Research output: Contribution to journalArticle

Abstract

We prove that every k-list-critical graph (k≥7) on n≥k+2 vertices has at least [Formula presented] (k−1+ [Formula presented])n edges where c=(k−3)([Formula presented] − [Formula presented]). This improves the bound established by Kostochka and Stiebitz [11]. The same bound holds for online k-list-critical graphs, improving the bound established by Riasat and Schauz [16]. Both bounds follow from a more general result stating that either a graph has many edges or it has an Alon-Tarsi orientable induced subgraph satisfying a certain degree condition.

Original languageEnglish (US)
JournalJournal of Combinatorial Theory. Series B
DOIs
StatePublished - Jan 1 2019

Fingerprint

Critical Graph
Lower bound
Degree Condition
Induced Subgraph
Graph in graph theory

Keywords

  • Critical
  • List coloring
  • Online list coloring

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Cite this

@article{4e62290826894e3c8e32517ff9541ef1,
title = "Improved lower bounds on the number of edges in list critical and online list critical graphs",
abstract = "We prove that every k-list-critical graph (k≥7) on n≥k+2 vertices has at least [Formula presented] (k−1+ [Formula presented])n edges where c=(k−3)([Formula presented] − [Formula presented]). This improves the bound established by Kostochka and Stiebitz [11]. The same bound holds for online k-list-critical graphs, improving the bound established by Riasat and Schauz [16]. Both bounds follow from a more general result stating that either a graph has many edges or it has an Alon-Tarsi orientable induced subgraph satisfying a certain degree condition.",
keywords = "Critical, List coloring, Online list coloring",
author = "Henry Kierstead and Landon Rabern",
year = "2019",
month = "1",
day = "1",
doi = "10.1016/j.jctb.2019.05.004",
language = "English (US)",
journal = "Journal of Combinatorial Theory. Series B",
issn = "0095-8956",
publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Improved lower bounds on the number of edges in list critical and online list critical graphs

AU - Kierstead, Henry

AU - Rabern, Landon

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We prove that every k-list-critical graph (k≥7) on n≥k+2 vertices has at least [Formula presented] (k−1+ [Formula presented])n edges where c=(k−3)([Formula presented] − [Formula presented]). This improves the bound established by Kostochka and Stiebitz [11]. The same bound holds for online k-list-critical graphs, improving the bound established by Riasat and Schauz [16]. Both bounds follow from a more general result stating that either a graph has many edges or it has an Alon-Tarsi orientable induced subgraph satisfying a certain degree condition.

AB - We prove that every k-list-critical graph (k≥7) on n≥k+2 vertices has at least [Formula presented] (k−1+ [Formula presented])n edges where c=(k−3)([Formula presented] − [Formula presented]). This improves the bound established by Kostochka and Stiebitz [11]. The same bound holds for online k-list-critical graphs, improving the bound established by Riasat and Schauz [16]. Both bounds follow from a more general result stating that either a graph has many edges or it has an Alon-Tarsi orientable induced subgraph satisfying a certain degree condition.

KW - Critical

KW - List coloring

KW - Online list coloring

UR - http://www.scopus.com/inward/record.url?scp=85068477510&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85068477510&partnerID=8YFLogxK

U2 - 10.1016/j.jctb.2019.05.004

DO - 10.1016/j.jctb.2019.05.004

M3 - Article

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

SN - 0095-8956

ER -