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JGT
2010
90views more  JGT 2010»
14 years 10 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
15 years 4 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»
14 years 11 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»
14 years 11 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»
14 years 10 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...