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Recognizing 3-colorable Basic Patterns on Planar Graphs

  • Guillermo De Ita LunaEmail author
  • Cristina López-Ramírez
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11524)

Abstract

We recognize the wheel graphs with different kinds of centers or axle faces as the basic pattern forming a planar graph. We focus on the analysis of the vertex-coloring for these graphic patterns, and identify cases for the 3 or 4 colorability of the wheels. We also consider different compositions among wheels and analyze its colorability process.

If a valid 3-coloring exists for the union of wheels G, then our proposal determines the constraints that a set of symbolic variables must hold. These constraints are expressed by a conjunctive normal form \(F_G\). We show that the satisfiability of \(F_G\) implies the existence of a valid 3-coloring for G. Otherwise, it is necessary to use 4 colors in order to properly color G. The revision of the satisfiability of \(F_G\) can be done in polynomial time by applying unit resolution and general properties from equalities and inequalities between symbolic variables.

Keywords

Wheel graphs Polyhedral wheel graphs Planar graphs Vertex coloring 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Guillermo De Ita Luna
    • 1
    Email author
  • Cristina López-Ramírez
    • 1
  1. 1.Fac. Cs. de la ComputaciónUniversidad Autónoma de PueblaPueblaMexico

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