Browsing Combinatorics and Optimization by Subject "edge coloring"

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Algebraic Analysis of Vertex-Distinguishing Edge-Colorings

Clark, David (University of Waterloo, 2006)

Vertex-distinguishing edge-colorings (vdec colorings) are a restriction of proper edge-colorings. These special colorings require that the sets of edge colors incident to every vertex be distinct. This is a relatively ...
Edge coloring multigraphs without small dense subsets

Haxell, P.E.; Kierstead, H.A. (Elsevier, 2015-12-06)

One consequence of a long-standing conjecture of Goldberg and Seymour about the chromatic index of multigraphs would be the following statement. Suppose $G$ is a multigraph with maximum degree $\Delta$, such that no vertex ...
Goldberg's conjecture is true for random multigraphs

Haxell, Penny; Krivelevich, Michael; Kronenberg, Gal (Elsevier, 2019-09)

In the 70s, Goldberg, and independently Seymour, conjectured that for any multigraph G, the chromatic index χ′(G) satisfies χ′(G) ≤ max{∆(G)+1,⌈ρ(G)⌉}, where ρ(G) = max\{\frac {e(G[S])}{\lfloor|S|/2\rfloor} \mid S\subseteq ...