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2013 | 33 | 1 | 181-192
Tytuł artykułu

Rainbow Connection In Sparse Graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
An edge-coloured connected graph G = (V,E) is called rainbow-connected if each pair of distinct vertices of G is connected by a path whose edges have distinct colours. The rainbow connection number of G, denoted by rc(G), is the minimum number of colours such that G is rainbow-connected. In this paper we prove that rc(G) ≤ k if |V (G)| = n and for all integers n and k with n − 6 ≤ k ≤ n − 3. We also show that this bound is tight.
Wydawca
Rocznik
Tom
33
Numer
1
Strony
181-192
Opis fizyczny
Daty
wydano
2013-03-01
online
2013-04-13
Twórcy
  • Computational Mathematics, Technische Universit¨at Braunschweig 38 023 Braunschweig, Germany, a.kemnitz@tu-bs.de
  • AGH University of Science and Technology al. A. Mickiewicza 30, 30-059 Krakow, Poland, mwozniak@agh.edu.pl
Bibliografia
  • [1] J.A. Bondy and U.S.R. Murty, Graph Theory (Springer, 2008). doi:10.1007/978-1-84628-970-5[Crossref]
  • [2] Y. Caro, A. Lev, Y. Roditty, Z. Tuza, and R. Yuster, On rainbow connection, Electron. J. Combin. 15 (2008) #57.
  • [3] S. Chakraborty, E. Fischer, A. Matsliah, and R. Yuster, Hardness and algorithms for rainbow connectivity, J. Comb. Optim. 21 (2011) 330-347. doi:10.1007/s10878-009-9250-9[Crossref]
  • [4] L.S. Chandran, A. Das, D. Rajendraprasad, and N.M. Varma, Rainbow connection number and connected dominating sets, J. Graph Theory 71 (2012) 206-218. doi:10.1002/jgt.20643[Crossref]
  • [5] G. Chartrand, G.L. Johns, K.A. McKeon, and P. Zhang, Rainbow connection in graphs, Math. Bohemica 133 (2008) 85-98.
  • [6] A.B. Ericksen, A matter of security, Graduating Engineer & Computer Careers (2007) 24-28.
  • [7] J. Ekstein, P. Holub, T. Kaiser, M. Koch, S. Matos Camacho, Z. Ryjáček and I. Schiermeyer, The rainbow connection number in 2-connected graphs, Discrete Math. doi:10.1016/j.disc.2012.04.022[WoS][Crossref]
  • [8] E. Győri, On division of graphs to connected subgraphs, Combinatorics, Vol. I, pp. 485-494, Colloq. Math. Soc. J´anos Bolyai, 18, North-Holland, Amsterdam, 1978.
  • [9] A. Kemnitz and I. Schiermeyer, Graphs with rainbow connection number two, Discuss. Math. Graph Theory 31 (2011) 313-320. doi:10.7151/dmgt.1547[Crossref]
  • [10] 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.[WoS]
  • [11] V.B. Le and Zs. Tuza, Finding optimal rainbow connection is hard, Preprint 2009.
  • [12] X. Li, M. Liu, and I. Schiermeyer, Rainbow connection number of dense graphs, to appear in Discuss. Math. Graph Theory. arXiv: 1110.5772v1 [math.CO] 2011
  • [13] X. Li and Y. Sun, Rainbow Connections of Graphs, Springer Briefs in Math., Springer, New York, 2012.
  • [14] L. Lovász, A homology theory for spanning trees of a graph, Acta Math. Hungar. 30 (1977) 241-251. doi:10.1007/BF01896190[Crossref]
  • [15] I. Schiermeyer, Rainbow connection in graphs with minimum degree three, Lecture Notes Computer Science 5874 (2009) 432-437. doi:10.1007/978-3-642-10217-2 42[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1640
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