Graphs with rainbow connection number two

• Autorzy: Arnfried Kemnitz , Ingo Schiermeyer
• Języki publikacji: EN

Abstrakty

EN

An edge-coloured graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colours. The rainbow connection number of a connected graph G, denoted rc(G), is the smallest number of colours that are needed in order to make G rainbow connected. In this paper we prove that rc(G) = 2 for every connected graph G of order n and size m, where $\binom{n-1}{2} + 1 ≤ m ≤ \binom{n}{2} - 1$. We also characterize graphs with rainbow connection number two and large clique number.

Słowa kluczowe

EN

edge colouring; rainbow colouring; rainbow connection

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs
• 05C35: Extremal problems

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2011
• Tom: 31
• Numer: 2
• Strony: 313-320

Daty

wydano

2011

otrzymano

2009-12-04

poprawiono

2010-05-12

zaakceptowano

2010-05-12

Twórcy

autor

Arnfried Kemnitz

• Computational Mathematics, Technische Universität Braunschweig, 38023 Braunschweig, Germany

autor

Ingo Schiermeyer

• Institut für Diskrete Mathematik und Algebra, Technische Universität Bergakademie Freiberg, 09596 Freiberg, Germany

Bibliografia

• [1] J.A. Bondy and U.S.R. Murty, Graph Theory (Springer, 2008), doi: 10.1007/978-1-84628-970-5.
• [2] S. Chakraborty, E. Fischer, A. Matsliah and R. Yuster, Hardness and algorithms for rainbow connectivity, Proceedings STACS 2009, to appear in Journal of Combinatorial Optimization.
• [3] Y. Caro, A. Lev, Y. Roditty, Z. Tuza and R. Yuster On rainbow connection, Electronic J. Combin. 15 (2008) #57.
• [4] G. Chartrand, G.L. Johns, K.A. McKeon and P. Zhang, Rainbow connection in graphs, Math. Bohemica 133 (2008) 85-98.
• [5] A.B. Ericksen, A matter of security, Graduating Engineer & Computer Careers (2007) 24-28.
• [6] M. Krivelevich and R. Yuster, The rainbow connection of a graph is (at most) reciprocal to its minimum degree, J. Graph Theory 63 (2010) 185-191.
• [7] V.B. Le and Z. Tuza, Finding optimal rainbow connection is hard, preprint 2009.
• [8] I. Schiermeyer, Rainbow connection in graphs with minimum degree three, IWOCA 2009, LNCS 5874 (2009) 432-437.

Identyfikatory

DOI

10.7151/dmgt.1547