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Journals and Conferences
A subgraph of an edge-colored graph is rainbow if all of its edges have different colors. For a graph H and a positive integer n, the anti-Ramsey number f(n, H) is the maximum number of colors in an edge-coloring of Kn with no rainbow copy of H . The rainbow number rb(n, H) is the minimum number of colors such that any edge-coloring of Kn with rb(n, H)… (More)
The Turán number ex(n,H) of H is the maximum number of edges of an n-vertex simple graph having no member ofH as a subgraph. We show lower and upper bounds for Turán numbers for disjoint copies of graphs.
The planar Ramsey number PR(G, H) is defined as the smallest integer n for which any 2-colouring of edges of Kn with red and blue, where red edges induce a planar graph, leads to either a red copy of G, or a blue H. In this note we study the weak induced version of the planar Ramsey number in the case when the second graph is complete.
The planar Ramsey number PR(G;H) is de ned as the smallest integer n for which any 2-colouring of edges of Kn with red and blue, where red edges induce a planar graph, leads to either a red copy of G, or a blue H . In this note we study the value of the planar Ramsey numbers, as well as their weak induced versions IPRw(G;H), for some classes of graphs. In… (More)