Almost-Rainbow Edge-Colorings of Some Small Subgraphs

Elliot Krop, and Irina Krop. "Almost-Rainbow Edge-Colorings of Some Small Subgraphs." Discussiones Mathematicae Graph Theory 33.4 (2013): 771-784. <http://eudml.org/doc/268325>.

@article{ElliotKrop2013,
abstract = {Let f(n, p, q) be the minimum number of colors necessary to color the edges of Kn so that every Kp is at least q-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 n ≢ 1(mod 3), f(n, 4, 5) ≤ n− 1. For a complete bipartite graph G= Kn,n, we show an n-color construction to color the edges of G so that every C4 ⊆ G is colored by at least three colors. This improves the best known upper bound of Axenovich, Füredi, and Mubayi.},
author = {Elliot Krop, Irina Krop},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {Ramsey theory; generalized Ramsey theory; rainbow-coloring; edge-coloring; Erdös problem; Erdős problem},
language = {eng},
number = {4},
pages = {771-784},
title = {Almost-Rainbow Edge-Colorings of Some Small Subgraphs},
url = {http://eudml.org/doc/268325},
volume = {33},
year = {2013},
}

TY - JOUR
AU - Elliot Krop
AU - Irina Krop
TI - Almost-Rainbow Edge-Colorings of Some Small Subgraphs
JO - Discussiones Mathematicae Graph Theory
PY - 2013
VL - 33
IS - 4
SP - 771
EP - 784
AB - Let f(n, p, q) be the minimum number of colors necessary to color the edges of Kn so that every Kp is at least q-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 n ≢ 1(mod 3), f(n, 4, 5) ≤ n− 1. For a complete bipartite graph G= Kn,n, we show an n-color construction to color the edges of G so that every C4 ⊆ G is colored by at least three colors. This improves the best known upper bound of Axenovich, Füredi, and Mubayi.
LA - eng
KW - Ramsey theory; generalized Ramsey theory; rainbow-coloring; edge-coloring; Erdös problem; Erdős problem
UR - http://eudml.org/doc/268325
ER -