Acyclic k choosability on planar graphs

André Raspaud

Description

Title Acyclic k-choosability on planar graphs Min Chen and André Raspaud LaBRI, Université Bordeaux 1, France JGA, November 5-6, 2009 Min Chen and André Raspaud (LaBRI) Acyclic k-choosability on planar graphs November 6, 2009 1 / 52

• graph induced


• ?uv ?


• color classes

Sujets

• University of Bordeaux

Informations

• Publié par: pefav
• Nombre de lectures: 25
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

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JGA, November 5-6, 2009

LaBRI, Université Bordeaux 1, France

2

Min Chen and André Raspaud

Acyclic k -choosability on planar graphs

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Our main theorem.

Definitions and some known results.

Conclusions and problems.

Outlines

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Definition: A proper k -coloring of the vertices of a graph G is a mapping π : V ( G ) → { 1 , ∙ ∙ ∙ , k } such that ∀ uv ∈ E ( G ) , π ( u ) 6 = π ( v ) .

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Definition: A proper k -coloring of the vertices of a graph G is a mapping π : V ( G ) → { 1 , ∙ ∙ ∙ , k } such that ∀ uv ∈ E ( G ) , π ( u ) 6 = π ( v ) .

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The acyclic chromatic number , denoted by χ a ( G ) , of a graph G , is the smallest integer k such that G has an acyclic k -coloring.

A proper vertex coloring of a graph is acyclic if the graph induced by the union of every two color classes is a forest .

A proper vertex coloring of a graph G is acyclic if there is no bicolored cycle in G .

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The acyclic coloring of graphs was introduced by Grünbaum in 1973.

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A proper vertex coloring of a graph is acyclic if the graph induced by the union of every two color classes is a forest .

A proper vertex coloring of a graph G is acyclic if there is no bicolored cycle in G .

595/2

The acyclic chromatic number , denoted by χ a ( G ) , of a graph G , is the smallest integer k such that G has an acyclic k -coloring.

The acyclic coloring of graphs was introduced by Grünbaum in 1973.

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DniefiontidnasemoswonksernultsDefinitions Accyilccloronig apgraranplontyliibasoohc-kcilcycRI)A(LaBpaudéRasnArdandnCnehiM

A proper vertex coloring of a graph G is acyclic if there is no bicolored cycle in G .

5/52

The acyclic coloring of graphs was introduced by Grünbaum in 1973.

The acyclic chromatic number , denoted by χ a ( G ) , of a graph G , is the smallest integer k such that G has an acyclic k -coloring.

A proper vertex coloring of a graph is acyclic if the graph induced by the union of every two color classes is a forest .

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