Browsing Waterloo Research by Author "Kronenberg, Gal"
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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 ... -
Ramsey-nice families of graphs
Aharoni, Ron; Alon, Noga; Amir, Michal; Haxell, Penny; Hefetz, Dan; Jiang, Zilin; Kronenberg, Gal; Naor, Alon (Elsevier, 2018-08)For a finite family $\cF$ of fixed graphs let $R_k(\cF)$ be the smallest integer $n$ for which every $k$-coloring of the edges of the complete graph $K_n$ yields a monochromatic copy of some $F\in\cF$. We say that $\cF$ ...