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JGT
2010
90views more  JGT 2010»
13 years 4 months ago
The rainbow connection of a graph is (at most) reciprocal to its minimum degree
An edge-colored graph G is rainbow edge-connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection of a connected graph G, deno...
Michael Krivelevich, Raphael Yuster
ISCOPE
1998
Springer
13 years 10 months ago
An Object-Oriented Collection of Minimum Degree Algorithms
The multiple minimum degree (MMD) algorithm and its variants have enjoyed 20+ years of research and progress in generating ll-reducing orderings for sparse, symmetric positive de n...
Gary Kumfert, Alex Pothen
JGT
2007
99views more  JGT 2007»
13 years 5 months ago
The upper bound of the number of cycles in a 2-factor of a line graph
Let G be a simple graph with order n and minimum degree at least two. In this paper, we prove that if every odd branch-bond in G has an edge-branch, then its line graph has a 2-fa...
Jun Fujisawa, Liming Xiong, Kiyoshi Yoshimoto, She...
CORR
2007
Springer
113views Education» more  CORR 2007»
13 years 5 months ago
Note on edge-colored graphs and digraphs without properly colored cycles
We study the following two functions: d(n, c) and d(n, c); d(n, c) (d(n, c)) is the minimum number k such that every c-edge-colored undirected (directed) graph of order n and mini...
Gregory Gutin
JGT
2010
81views more  JGT 2010»
13 years 4 months ago
Cycles and paths in edge-colored graphs with given degrees
Sufficient degree conditions for the existence of properly edge-colored cycles and paths in edge-colored graphs, multigraphs and random graphs are inverstigated. In particular, we...
A. Abouelaoualim, Kinkar Chandra Das, Wenceslas Fe...