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90views more  JGT 2010»
12 years 1 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
93views Education» more  CORR 2002»
12 years 3 months ago
On the Reflexivity of Point Sets
We introduce a new measure for planar point sets S that captures a combinatorial distance that S is from being a convex set: The reflexivity (S) of S is given by the smallest numb...
Esther M. Arkin, Sándor P. Fekete, Ferran H...
136views more  CPC 2004»
12 years 3 months ago
On the Strong Chromatic Number
The strong chromatic number, S(G), of an n-vertex graph G is the smallest number k such that after adding kn/k-n isolated vertices to G and considering any partition of the vertic...
Penny E. Haxell
68views more  APPML 2005»
12 years 3 months ago
A note on edge fault tolerance with respect to hypercubes
In the previous studies on k-edge fault tolerance with respect to hypercubes Qn, matrices for generating linear k-EFT(Qn) graphs were used. Let EFTL(n, k) denote the set of matric...
Tung-Yang Ho, Ting-Yi Sung, Lih-Hsing Hsu
153views more  DAM 2007»
12 years 3 months ago
Computing the minimum number of hybridization events for a consistent evolutionary history
It is now well-documented that the structure of evolutionary relationships between a set of present-day species is not necessarily tree-like. The reason for this is that reticulat...
Magnus Bordewich, Charles Semple
91views Education» more  CORR 2007»
12 years 3 months ago
Single-Exclusion Number and the Stopping Redundancy of MDS Codes
—For a linear block code C, its stopping redundancy is defined as the smallest number of check nodes in a Tanner graph for C, such that there exist no stopping sets of size smal...
Junsheng Han, Paul H. Siegel, Ron M. Roth
91views more  JGT 2008»
12 years 3 months ago
On the editing distance of graphs
An edge-operation on a graph G is defined to be either the deletion of an existing edge or the addition of a nonexisting edge. Given a family of graphs G, the editing distance fro...
Maria Axenovich, André E. Kézdy, Rya...
114views more  COMBINATORICS 2006»
12 years 3 months ago
The Maximum Distinguishing Number of a Group
Let G be a group acting faithfully on a set X. The distinguishing number of the action of G on X, denoted DG(X), is the smallest number of colors such that there exists a coloring...
Melody Chan
107views more  AIR 2006»
12 years 3 months ago
Just enough learning (of association rules): the TAR2 "Treatment" learner
Abstract. An over-zealous machine learner can automatically generate large, intricate, theories which can be hard to understand. However, such intricate learning is not necessary i...
Tim Menzies, Ying Hu
139views more  DM 2008»
12 years 3 months ago
On domination and reinforcement numbers in trees
The reinforcement number of a graph is the smallest number of edges that have to be added to a graph to reduce the domination number. We introduce the k-reinforcement number of a ...
Jean R. S. Blair, Wayne Goddard, Stephen T. Hedetn...