Graph folding and chromatic number

• Campena, Francis Joseph ^[1] ; Gervacio, Severino ^[1]
  1. [1] La Salle University

     La Salle University

     City of Philadelphia, Estados Unidos

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 42, Nº. 4, 2023, págs. 957-965
• Idioma: inglés
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• Resumen

  • Given a connected graph G, identify two vertices if they have a common neighbor and then reduce the resulting multiple edges to simple edges. Repeat the process until the result is a complete graph. This process is called folding a graph.

    We show here that any connected graph G which is not complete folds onto the connected graph Kp where p = χ(G), the chromatic number of G. Furthermore, the set of all integers p such that G folds onto Kp consist of consecutive integers, the smallest of which is χ(G).

    One particular result of this study is that a sharp upper bound was obtained on the largest complete graph which a graph can be folded onto.