Note: Hajós' conjecture for line graphs

  • Authors:

  • Carsten Thomassen

  • Affiliations:

  • Department of Mathematics, Technical University of Denmark, DK-2800 Lyngby, Denmark

  • Venue:
  • Journal of Combinatorial Theory Series B
  • Year:
  • 2007

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Abstract

We prove that, if a graph G (without multiple edges) has maximum degree d and edge-chromatic number d+1, then G contains two distinct vertices x,y and a collection of d pairwise edge-disjoint paths between x and y. In particular, the line graph of G satisfies Hajos' conjecture.