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|Abstract:||Reed’s omega, Delta, chi conjecture proposes that every graph satisfies chi <= inverted right perpendicular1/2 (Delta + 1 + omega)inverted left perpendicular; it is known to hold for all claw-free graphs. In this paper we consider a local strengthening of this conjecture. We prove the local strengthening for line graphs, then note that previous results immediately tell us that the local strengthening holds for all quasi-line graphs. Our proofs lead to polytime algorithms for constructing colorings that achieve our bounds: O(n(2)) for line graphs and O(n(3)m(2)) for quasi-line graphs. For line graphs, this is faster than the best known algorithm for constructing a coloring that achieves the bound of Reed’s original conjecture.|
|Electronic Publication Date:||17-Jan-2013|
|Citation:||Chudnovsky, Maria, King, Andrew D, Plumettaz, Matthieu, Seymour, Paul. (2013). A LOCAL STRENGTHENING OF REED’S omega, Delta, chi CONJECTURE FOR QUASI- LINE GRAPHS. SIAM JOURNAL ON DISCRETE MATHEMATICS, 27 (95 - 108. doi:10.1137/110847585|
|Pages:||95 - 108|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||SIAM JOURNAL ON DISCRETE MATHEMATICS|
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