4 research outputs found
Almost-rainbow edge-colorings of some small subgraphs
Let be the minimum number of colors necessary to color the edges
of so that every is at least -colored. We improve current bounds
on the {7/4}n-3{5/6}n+1\leq
f(n,4,5)n\not\equiv 1 \pmod 3f(n,4,5)\leq n-1G=K_{n,n}GC_4\subseteq G$ is colored by at least three
colors. This improves the best known upper bound of M. Axenovich, Z. F\"uredi,
and D. Mubayi.Comment: 13 page
Almost-Rainbow Edge-Colorings of Some Small Subgraphs
Let be the minimum number of colors necessary to color the edges of so that every is at least -colored. We improve current bounds on these nearly “anti-Ramsey” numbers, first studied by Erdös and Gyárfás. We show that , slightly improving the bound of Axenovich. We make small improvements on bounds of Erdös and Gyárfás by showing and for all even , . For a complete bipartite graph , we show an -color construction to color the edges of so that every is colored by at least three colors. This improves the best known upper bound of Axenovich, Füredi, and Mubayi