Approximating the chromatic index of multigraphs

  title={Approximating the chromatic index of multigraphs},
  author={Guantao Chen and Xingxing Yu and Wenan Zang},
  journal={Journal of Combinatorial Optimization},
  • Guantao Chen, Xingxing Yu, Wenan Zang
  • Published 2011
  • Mathematics, Computer Science
  • Journal of Combinatorial Optimization
AbstractIt is well known that if G is a multigraph then χ′(G)≥χ′*(G):=max {Δ(G),Γ(G)}, where χ′(G) is the chromatic index of G, χ′*(G) is the fractional chromatic index of G, Δ(G) is the maximum degree of G, and Γ(G)=max {2|E(G[U])|/(|U|−1):U⊆V(G),|U|≥3, |U| is odd}. The conjecture that χ′(G)≤max {Δ(G)+1,⌈Γ(G)⌉} was made independently by Goldberg (Discret. Anal. 23:3–7, 1973), Anderson (Math. Scand. 40:161–175, 1977), and Seymour (Proc. Lond. Math. Soc. 38:423–460, 1979). Using a probabilistic… Expand
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