Hadwiger's conjecture for line graphs

  • Authors:

  • Bruce Reed;Paul Seymour

  • Affiliations:

  • Equipe Combinatoire, Case 189, Université/ de Paris VI, 4 Place Jussieu, 75252 Paris Cedex 05, France;Department of Mathematics, Princeton University/ Princeton, NJ

  • Venue:
  • European Journal of Combinatorics - Special issue: Topological graph theory
  • Year:
  • 2004

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Abstract

We prove that Hadwiger's conjecture holds for line graphs. Equivalently, we show that for every loopless graph G (possibly with parallel edges) and every integer k ≥ 0, either G is k-edge-colourable, or there are k + 1 connected subgraphs A1....,Ak+1 of G, each with at least one edge, such that E(Ai ∩ Aj) = 0 and V(Ai ∩ Aj) ≠ 0 for 1 ≤ i