Opuscula Math. 37, no. 4 (2017), 567-575

Opuscula Mathematica

Anti-Ramsey numbers for disjoint copies of graphs

Izolda Gorgol
Agnieszka Görlich

Abstract. A subgraph of an edge-colored graph is called rainbow if all of its edges have different colors. For a graph \(G\) and a positive integer \(n\), the anti-Ramsey number \(ar(n,G)\) is the maximum number of colors in an edge-coloring of \(K_n\) with no rainbow copy of \(H\). Anti-Ramsey numbers were introduced by Erdȍs, Simonovits and Sós and studied in numerous papers. Let \(G\) be a graph with anti-Ramsey number \(ar(n,G)\). In this paper we show the lower bound for \(ar(n,pG)\), where \(pG\) denotes \(p\) vertex-disjoint copies of \(G\). Moreover, we prove that in some special cases this bound is sharp.

Keywords: anti-Ramsey number, rainbow number, disjoint copies.

Mathematics Subject Classification: 05C55, 05C15.

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  • Izolda Gorgol
  • Lublin University of Technology, Department of Applied Mathematics, Nadbystrzycka 38D, 20-618 Lublin, Poland
  • Agnieszka Görlich
  • AGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Krakow, Poland
  • Communicated by Ingo Schiermeyer.
  • Received: 2016-03-10.
  • Revised: 2016-07-20.
  • Accepted: 2016-08-06.
  • Published online: 2017-04-28.
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Cite this article as:
Izolda Gorgol, Agnieszka Görlich, Anti-Ramsey numbers for disjoint copies of graphs, Opuscula Math. 37, no. 4 (2017), 567-575, http://dx.doi.org/10.7494/OpMath.2017.37.4.567

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