Proper connection of graphs

Valentin Borozan, Shinya Fujita, Aydin Gerek, Colton Magnant, Yannis Manoussakis, Leandro Montero, Z. Tuza

Research output: Contribution to journalArticle

42 Citations (Scopus)

Abstract

An edge-colored graph G is k-proper connected if every pair of vertices is connected by k internally pairwise vertex-disjoint proper colored paths. The k-proper connection number of a connected graph G, denoted by p ck(G), is the smallest number of colors that are needed to color the edges of G in order to make it k-proper connected. In this paper we prove several upper bounds for p ck(G). We state some conjectures for general and bipartite graphs, and we prove them for the case when k=1. In particular, we prove a variety of conditions on G which imply p c1(G)=2.

Original languageEnglish
Pages (from-to)2550-2560
Number of pages11
JournalDiscrete Mathematics
Volume312
Issue number17
DOIs
Publication statusPublished - Sep 6 2012

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Color
Graph in graph theory
Edge-colored Graph
Bipartite Graph
Connected graph
Pairwise
Disjoint
Upper bound
Imply
Path
Vertex of a graph

Keywords

  • Proper coloring
  • Proper connection

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Borozan, V., Fujita, S., Gerek, A., Magnant, C., Manoussakis, Y., Montero, L., & Tuza, Z. (2012). Proper connection of graphs. Discrete Mathematics, 312(17), 2550-2560. https://doi.org/10.1016/j.disc.2011.09.003

Proper connection of graphs. / Borozan, Valentin; Fujita, Shinya; Gerek, Aydin; Magnant, Colton; Manoussakis, Yannis; Montero, Leandro; Tuza, Z.

In: Discrete Mathematics, Vol. 312, No. 17, 06.09.2012, p. 2550-2560.

Research output: Contribution to journalArticle

Borozan, V, Fujita, S, Gerek, A, Magnant, C, Manoussakis, Y, Montero, L & Tuza, Z 2012, 'Proper connection of graphs', Discrete Mathematics, vol. 312, no. 17, pp. 2550-2560. https://doi.org/10.1016/j.disc.2011.09.003
Borozan V, Fujita S, Gerek A, Magnant C, Manoussakis Y, Montero L et al. Proper connection of graphs. Discrete Mathematics. 2012 Sep 6;312(17):2550-2560. https://doi.org/10.1016/j.disc.2011.09.003
Borozan, Valentin ; Fujita, Shinya ; Gerek, Aydin ; Magnant, Colton ; Manoussakis, Yannis ; Montero, Leandro ; Tuza, Z. / Proper connection of graphs. In: Discrete Mathematics. 2012 ; Vol. 312, No. 17. pp. 2550-2560.
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