Graphs with 3-Rainbow Index n − 1 and n − 2

@article{XueliangLi2015,
abstract = {Let G = (V (G),E(G)) be a nontrivial connected graph of order n with an edge-coloring c : E(G) → \{1, 2, . . . , q\}, q ∈ N, where adjacent edges may be colored the same. A tree T in G is a rainbow tree if no two edges of T receive the same color. For a vertex set S ⊆ V (G), a tree connecting S in G is called an S-tree. The minimum number of colors that are needed in an edge-coloring of G such that there is a rainbow S-tree for each k-subset S of V (G) is called the k-rainbow index of G, denoted by rxk(G), where k is an integer such that 2 ≤ k ≤ n. Chartrand et al. got that the k-rainbow index of a tree is n−1 and the k-rainbow index of a unicyclic graph is n−1 or n−2. So there is an intriguing problem: Characterize graphs with the k-rainbow index n − 1 and n − 2. In this paper, we focus on k = 3, and characterize the graphs whose 3-rainbow index is n − 1 and n − 2, respectively.},
author = {Xueliang Li, Ingo Schiermeyer, Kang Yang, Yan Zhao},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {rainbow S-tree; k-rainbow index; rainbow -tree; -rainbow index},
language = {eng},
number = {1},
pages = {105-120},
title = {Graphs with 3-Rainbow Index n − 1 and n − 2},
url = {http://eudml.org/doc/271224},
volume = {35},
year = {2015},
}

TY - JOUR
AU - Xueliang Li
AU - Ingo Schiermeyer
AU - Kang Yang
AU - Yan Zhao
TI - Graphs with 3-Rainbow Index n − 1 and n − 2
JO - Discussiones Mathematicae Graph Theory
PY - 2015
VL - 35
IS - 1
SP - 105
EP - 120
AB - Let G = (V (G),E(G)) be a nontrivial connected graph of order n with an edge-coloring c : E(G) → {1, 2, . . . , q}, q ∈ N, where adjacent edges may be colored the same. A tree T in G is a rainbow tree if no two edges of T receive the same color. For a vertex set S ⊆ V (G), a tree connecting S in G is called an S-tree. The minimum number of colors that are needed in an edge-coloring of G such that there is a rainbow S-tree for each k-subset S of V (G) is called the k-rainbow index of G, denoted by rxk(G), where k is an integer such that 2 ≤ k ≤ n. Chartrand et al. got that the k-rainbow index of a tree is n−1 and the k-rainbow index of a unicyclic graph is n−1 or n−2. So there is an intriguing problem: Characterize graphs with the k-rainbow index n − 1 and n − 2. In this paper, we focus on k = 3, and characterize the graphs whose 3-rainbow index is n − 1 and n − 2, respectively.
LA - eng
KW - rainbow S-tree; k-rainbow index; rainbow -tree; -rainbow index
UR - http://eudml.org/doc/271224
ER -