Results 1  10
of
748
The Vertex Separation And Search Number Of A Graph
"... We relate two concepts in graph theory and algorithmic complexity, namely the search number and the vertex separation of a graph. Let s (G ) denote the search number and vs (G ) denote the vertex separation of a connected, undirected graph G . We show that vs (G ) s (G ) vs (G ) + 2 and we give a ..."
Abstract

Cited by 88 (1 self)
 Add to MetaCart
We relate two concepts in graph theory and algorithmic complexity, namely the search number and the vertex separation of a graph. Let s (G ) denote the search number and vs (G ) denote the vertex separation of a connected, undirected graph G . We show that vs (G ) s (G ) vs (G ) + 2 and we give a
A GraphTheoretic Game and its Application to the kServer Problem
 SIAM J. COMPUT
, 1995
"... This paper investigates a zerosum game played on a weighted connected graph G between two players, the tree player and the edge player. At each play, the tree player chooses a spanning tree T and the edge player chooses an edge e. The payoff to the edge player is cost(T; e), defined as follows: If ..."
Abstract

Cited by 139 (4 self)
 Add to MetaCart
This paper investigates a zerosum game played on a weighted connected graph G between two players, the tree player and the edge player. At each play, the tree player chooses a spanning tree T and the edge player chooses an edge e. The payoff to the edge player is cost(T; e), defined as follows
On vertex sparsifiers with Steiner nodes
 In 44th symposium on Theory of Computing
, 2012
"... Given an undirected graph G = (V, E) with edge capacities ce ≥ 1 for e ∈ E and a subset T of k vertices called terminals, we say that a graph H is a qualityq cut sparsifier for G iff T ⊆ V (H), and for any partition (A, B) of T, the values of the minimum cuts separating A and B in graphs G and H ar ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
Given an undirected graph G = (V, E) with edge capacities ce ≥ 1 for e ∈ E and a subset T of k vertices called terminals, we say that a graph H is a qualityq cut sparsifier for G iff T ⊆ V (H), and for any partition (A, B) of T, the values of the minimum cuts separating A and B in graphs G and H
The vertex sizeRamsey number
, 2015
"... In this paper, we study an analogue of sizeRamsey numbers for vertex colorings. For a given number of colors r and a graph G the vertex sizeRamsey number of G, denoted by R̂v(G, r), is the least number of edges in a graph H with the property that any rcoloring of the vertices of H yields a monoch ..."
Abstract
 Add to MetaCart
monochromatic copy of G. We observe that Ωr(∆n) = R̂v(G, r) = Or(n 2) for any G of order n and maximum degree ∆, and prove that for some graphs these bounds are tight. On the other hand, we show that even 3regular graphs can have nonlinear vertex sizeRamsey numbers. Finally, we prove that R̂v(T, r) = Or
Note on VertexDisjoint Cycles
, 1998
"... this paper, it is shown that if G is a graph of average degree at least k 2 + 19k + 12 and suciently many vertices, then G contains vertexdisjoint cycles of k consecutive even lengths, answering the above question in the armative. The coecient of k 2 cannot be decreased and, in this sense, this ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
this paper, it is shown that if G is a graph of average degree at least k 2 + 19k + 12 and suciently many vertices, then G contains vertexdisjoint cycles of k consecutive even lengths, answering the above question in the armative. The coecient of k 2 cannot be decreased and, in this sense
The L(2,1)Labeling Problem on Graphs
, 1993
"... An L(2; 1)labeling of a graph G is a function f from the vertex set V (G) to the set of all nonnegative integers such that jf(x) 0 f(y)j 2 if d(x; y) = 1 and jf(x) 0 f(y)j 1 if d(x; y) = 2. The L(2; 1)labeling number (G) of G is the smallest number k such that G has a L(2; 1)labeling with max ..."
Abstract

Cited by 108 (2 self)
 Add to MetaCart
An L(2; 1)labeling of a graph G is a function f from the vertex set V (G) to the set of all nonnegative integers such that jf(x) 0 f(y)j 2 if d(x; y) = 1 and jf(x) 0 f(y)j 1 if d(x; y) = 2. The L(2; 1)labeling number (G) of G is the smallest number k such that G has a L(2; 1)labeling
Vertex Fault Tolerant Additive Spanners
, 2014
"... A faulttolerant structure for a network is required to continue functioning following the failure of some of the network’s edges or vertices. In this paper, we address the problem of designing a faulttolerant additive spanner, namely, a subgraph H of the network G such that subsequent to the failu ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
to the failure of a single vertex, the surviving part of H still contains an additive spanner for (the surviving part of) G, satisfying dist(s, t,H \ {v}) ≤ dist(s, t,G \ {v}) + β for every s, t, v ∈ V. Recently, the problem of constructing faulttolerant additive spanners resilient to the failure of up to f
Local characteristics, entropy and limit theorems for spanning trees and domino tilings via transferimpedances
, 1993
"... Let G be a finite graph or an infinite graph on which Z d acts with finite fundamental domain. If G is finite, let T be a random spanning tree chosen uniformly from all spanning trees of G; if G is infinite, methods from [Pem] show that this still makes sense, producing a random essential spanning f ..."
Abstract

Cited by 112 (2 self)
 Add to MetaCart
Let G be a finite graph or an infinite graph on which Z d acts with finite fundamental domain. If G is finite, let T be a random spanning tree chosen uniformly from all spanning trees of G; if G is infinite, methods from [Pem] show that this still makes sense, producing a random essential spanning
Forbidden Pairs for VertexDisjoint Claws
"... Let k ≥ 4, and let H1,H2 be connected graphs with V (Hi)  ≥ 3 for i = 1, 2. A graph G is said to be {H1,...,Hl}free if none of H1,...,Hl is an induced subgraph of G. We prove that if there exists a positive integer n0 such that every {H1,H2}free graph G with V (G)  ≥ n0 and δ(G) ≥ 3 contains ..."
Abstract
 Add to MetaCart
contains k vertexdisjoint claws, then {H1,H2}∩{K1,t  t ≥ 2} � = ∅. Also, we prove that every K1,rfree graph of sufficiently large order with minimum degree at least t contains k vertexdisjoint copies of K1,t.
On the Complexity of VertexDisjoint LengthRestricted Path Problems
, 1998
"... Let G = (V; E) be a simple graph and s and t be two distinct vertices of G. A path in G is called `bounded for some ` 2 N , if it does not contain more than ` edges. We study the computational complexity of approximating the optimum value for two optimization problems of finding sets of vertexd ..."
Abstract

Cited by 16 (0 self)
 Add to MetaCart
disjoint `bounded s; tpaths in G. First, we show that computing the maximum number of vertexdisjoint `bounded s; tpaths is APX complete for any fixed length bound ` 5. Second, for a given number k 2 N , 1 k jV j \Gamma 1, and nonnegative weights on the edges of G, the problem of finding k vertex
Results 1  10
of
748