Asymptotics of the Chromatic Index for Multigraphs
نویسندگان
چکیده
منابع مشابه
Asymptotics of the total chromatic number for multigraphs
For loopless multigraphs, the total chromatic number is asymptotically its fractional counterpart as the latter invariant tends to infinity. The proof of this is based on a recent theorem of Kahn establishing the analogous asymptotic behaviour of the list-chromatic index for multigraphs. The total colouring conjecture, proposed independently by Behzad [1] and Vizing [11], asserts that the total...
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It is well known that if G is a multigraph then χ(G) ≥ χ(G) := max{∆(G), Γ(G)}, where χ(G) is the chromatic index of G, χ(G) is the fractional chromatic index of G, ∆(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{∆(G) + 1, dΓ(G)e} was made independently by Goldberg (1973), Anderson (1977), and Seymour (19...
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A multigraph M with maximum degree (M) is called critical, if the chromatic index 0 (M) > (M) and 0 (M ? e) = 0 (M) ? 1 for each edge e of M. The weak critical graph conjecture 1, 7] claims that there exists a constant c > 0 such that every critical multigraph M with at most c (M) vertices has odd order. We disprove this conjecture by constructing critical multigraphs of order 20 with maximum d...
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For any multigraph G of order n, let Φ(G) denote the integer roundup of its fractional chromatic index. We show that the chomatic index χ (G) satisfies χ (G) ≤ Φ(G) + log(min{ n + 1 3 , Φ(G)}). The method used is deterministic (though it extends a famous probabilistic result by Kahn), and different from the re-coloring techniques that are the basis for many of the other known upper bounds on χ ...
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The integer round-up 4(G) of the fractional chromatic index yields the standard lower bound for the chromatic index of a multigraph G. We show that if G has even order n, then the chromatic index exceeds 4(G) by at most max{log,,, n, 1 + n/30}. More generally, we show that for any real b, 2/3 <b < 1, the chromatic index of G exceeds 4(G) by at most max{log,,b n, 1 +n(l b)/lO}. This is used to s...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1996
ISSN: 0095-8956
DOI: 10.1006/jctb.1996.0067