Rainbow Numbers for Cycles with Pendant Edges |
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Authors: | Izolda Gorgol |
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Institution: | (1) Department of Applied Mathematics, Lublin University of Technology, Nadbystrzycka 38D, 20-618 Lublin, Poland |
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Abstract: | A subgraph of an edge-colored graph is called 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 K
n
with no rainbow copy of H. The rainbow number
rb(n, H) is the minimum number of colors such that any edge-coloring of K
n
with rb(n, H) number of colors contains a rainbow copy of H. Certainly rb(n, H) = f(n, H) + 1. Anti-Ramsey numbers were introduced by Erdős et al. 4] and studied in numerous papers.
We show that for n ≥ k + 1, where C
k
+ denotes a cycle C
k
with a pendant edge. |
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Keywords: | Rainbow number anti-Ramsey number |
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