Local k-colorings of graphs and hypergraphs
Journal of Combinatorial Theory Series B
Local and mean k-Ramsey numbers for complete graphs
Journal of Graph Theory
Random Graphs 93 Proceedings of the sixth international seminar on Random graphs and probabilistic methods in combinatorics and computer science
Properly colored Hamilton cycles in edge-colored complete graphs
Random Structures & Algorithms
Constrained Ramsey numbers of graphs
Journal of Graph Theory
Rainbow Arithmetic Progressions and Anti-Ramsey Results
Combinatorics, Probability and Computing
Combinatorics, Probability and Computing
Combinatorics, Probability and Computing
Sufficient conditions for the existence of perfect heterochromatic matchings in colored graphs
CJCDGCGT'05 Proceedings of the 7th China-Japan conference on Discrete geometry, combinatorics and graph theory
Properly coloured copies and rainbow copies of large graphs with small maximum degree
Random Structures & Algorithms
Color degree and heterochromatic cycles in edge-colored graphs
European Journal of Combinatorics
Rainbow Turán problem for even cycles
European Journal of Combinatorics
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We consider a canonical Ramsey type problem. An edge-coloring of a graph is called m-good if each color appears at most m times at each vertex. Fixing a graph G and a positive integer m, let f(m, G) denote the smallest n such that every m-good edge-coloring of Kn, yields a properly edge-colored copy of G, and let g(m, G) denote the smallest n such that every m-good edge-coloring of Kn yields a rainbow copy of G. We give bounds on f(m, G) and g(m, G). For complete graphs G = Kt, we have c1mt2/ln t ≤ f(m, Kt) ≤ c2mt2, and c'1mt3/ln t ≤ g(m, Kt) ≤ c'2mt3/ln t, where c1, c2, c'1, c'2 are absolute constants. We also give bounds on f(m, G) and g(m, G) for general graphs G in terms of degrees in G. In particular, we show that for fixed m and d, and all sufficiently large n compared to m and d, f(m, G) = n for all graphs G with n vertices and maximum degree at most d.