Browsing Mathematics (Faculty of) by Author "Haxell, Penny"
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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 ... -
A note on intersecting hypergraphs with large cover number
Haxell, P.E.; Scott, A.D. (The Electronic Journal of Combinatorics, 2017-08-11)We give a construction of r-partite r-uniform intersecting hypergraphs with cover number at least r−4 for all but finitely many r. This answers a question of Abu-Khazneh, Barát, Pokrovskiy and Szabó, and shows that a ... -
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 $\cF$ ... -
A Stability Theorem for Matchings in Tripartite 3-Graphs
Haxell, Penny; Narins, Lothar (Cambridge University Press, 2018-04-02)It follows from known results that every regular tripartite hypergraph of positive degree, with n vertices in each class, has matching number at least n/2. This bound is best possible, and the extremal configuration is ...