Achieving maximum chromatic index in multigraphs
نویسندگان
چکیده
منابع مشابه
Approximating the chromatic index of multigraphs
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...
متن کاملChromatic-index critical multigraphs of order 20
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...
متن کاملA Combined Logarithmic Bound on the Chromatic Index of Multigraphs
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 ...
متن کاملA sublinear bound on the chromatic index of multigraphs
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...
متن کاملOn the list chromatic index of nearly bipartite multigraphs
Galvin ([7]) proved that every k-edge-colorable bipartite multigraph is kedge-choosable. Slivnik ([11]) gave a streamlined proof of Galvin's result. A multigraph G is said to be nearly bipartite if it contains a special vertex Vs such that G Vs is a bipartite multigraph. We use the technique in Slivnik's proof to obtain a list coloring analog of Vizing's theorem ([12]) for nearly bipartite mult...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2008.04.023