TY - JOUR

T1 - Rainbow connection for some families of hypergraphs

AU - Silva, Manuel Almeida

AU - Sousa, Teresa Maria Jerónimo

AU - Liu, Henry Chung Hang

PY - 2014/1/1

Y1 - 2014/1/1

N2 - An edge-coloured path in a graph is rainbow if its edges have distinct colours. The rainbow connection number of a connected graph G, denoted by rc(G), is the minimum number of colours required to colour the edges of G so that any two vertices of G are connected by a rainbow path. The function rc(G) was first introduced by Chartrand et al. [Math. Bohem., 133 (2008), pp. 85-98], and has since attracted considerable interest. In this paper, we introduce two extensions of the rainbow connection number to hypergraphs. We study these two extensions of the rainbow connection number in minimally connected hypergraphs, hypergraph cycles and complete multipartite hypergraphs.

AB - An edge-coloured path in a graph is rainbow if its edges have distinct colours. The rainbow connection number of a connected graph G, denoted by rc(G), is the minimum number of colours required to colour the edges of G so that any two vertices of G are connected by a rainbow path. The function rc(G) was first introduced by Chartrand et al. [Math. Bohem., 133 (2008), pp. 85-98], and has since attracted considerable interest. In this paper, we introduce two extensions of the rainbow connection number to hypergraphs. We study these two extensions of the rainbow connection number in minimally connected hypergraphs, hypergraph cycles and complete multipartite hypergraphs.

KW - rainbow connection number

KW - hypergraph colouring

KW - Graph colouring

U2 - 10.1016/j.disc.2014.03.013

DO - 10.1016/j.disc.2014.03.013

M3 - Article

VL - 327

SP - 40

EP - 50

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - NA

ER -