A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Factor domination and minimum degree

2003
*
Discrete Mathematics
*

In this paper, we give bounds on (F1; F2; : : : ; F k ) in terms of the

doi:10.1016/s0012-365x(02)00522-8
fatcat:p3x42xbkove5xkvbnlrl7yrp7u
*minimum**degrees*of the Fi. ... The cardinality of a smallest such set is called the*factor**domination*number of F1; F2; : : : ; F k*and*denoted by (F1; F2; : : : ; F k ). ... In this paper, we give bounds on the*factor**domination*number in terms of the order*and*the*minimum**degrees*of the*factors*. Our notation is as follows. ...##
###
Exact Algorithms for Finding the Minimum Independent Dominating Set in Graphs
[chapter]

2006
*
Lecture Notes in Computer Science
*

In this paper, we consider the

doi:10.1007/11940128_45
fatcat:xudwusz3szabncfujetovhuyea
*Minimum*Independent*Dominating*Set problem*and*develop exact exponential algorithms that break the trivial developed to solve this problem on general graphs. ... For sparse graphs, e.g. graphs with*degree*bounded by 3*and*4, we show that a few new branching techniques can be applied to these graphs*and*the resulting algorithms have time complexities O * (2 0.465 ... Acknowledgment We thank the anonymous reviewers for their comments*and*suggestions on an earlier version of the paper. ...##
###
Simultaneous graph parameters: Factor domination and factor total domination

2006
*
Discrete Mathematics
*

A subset S ⊆ V is a

doi:10.1016/j.disc.2006.04.017
fatcat:blf4n5gqovahjb4zmw6uwynfbe
*factor**dominating*set if in every F i every vertex not in S is adjacent to a vertex in S,*and*a*factor*total*dominating*set if in every F i every vertex in V is adjacent to a vertex ... The cardinality of a smallest such set is the*factor*(total)*domination*number. In this note we investigate bounds on the*factor*(total)*domination*number. ... Surprisingly perhas, the best bounds for*minimum**degree*3*and**minimum**degree*4 come from two different sources. ...##
###
Star-Uniform Graphs

2010
*
Graphs and Combinatorics
*

In this paper, we show that a graph is star-uniform if

doi:10.1007/s00373-010-0917-x
fatcat:d4vldnfbbbgfpaqklsps7ffxqm
*and*only if has equal*domination**and*matching number. ... Motivated by the*minimum*cost spanning tree*and*the optimal assignment problems, Hartnell*and*Rall posed an open problem to characterize all the star-uniform graphs. ... Acknowledgments The authors are indebted to the anonymous referees for their many helpful*and*constructive suggestions. ...##
###
Complexity of majority monopoly and signed domination problems

2012
*
Journal of Discrete Algorithms
*

We show that

doi:10.1016/j.jda.2011.12.019
fatcat:zcrilcdbjnhmzczcay2hu7esei
*minimum*majority monopoly problem is APX-complete for graphs with*degree*at most 3*and*at least 2*and**minimum*signed*domination*problem is APX-complete, for 3-regular graphs. ... We consider approximability of two natural variants of classical*dominating*set problem, namely*minimum*majority monopoly*and**minimum*signed*domination*. ... Acknowledgement The author thanks the anonymous referees for their valuable comments*and*suggestions that helped to improve the clarity, correctness*and*presentation of the proofs. ...##
###
Page 2455 of Mathematical Reviews Vol. , Issue 2000d
[page]

2000
*
Mathematical Reviews
*

Let k >2

*and*let G be a graph of order m with*minimum**degree*at least k,*and*with n > 8k — 16 for even n,*and*n > 6k — 13 for odd n. ... Those vertices that belong to no*minimum**dominating*set are also investigated*and*characterized when the graphs are trees. ...##
###
Fast Algorithms for min independent dominating set
[chapter]

2010
*
Lecture Notes in Computer Science
*

Gaspers

doi:10.1007/978-3-642-13284-1_20
fatcat:b2jv2ad4ffejdjedgkjlamlzsm
*and*M. Liedloff, A branch-*and*-reduce algorithm for finding a*minimum*independent*dominating*set in graphs, Proc. WG'06). ... We first devise a branching algorithm that computes a*minimum*independent*dominating*set on any graph with running time O*(2^0.424n)*and*polynomial space. This improves the O*(2^0.441n) result by (S. ... For the*degree*of v, we use the notation : v ∈ H}. We use δ*and*∆ to denote the*minimum**and*maximum*degree*of G, respectively. ...##
###
Factoring matrices with a tree-structured sparsity pattern

2011
*
Linear Algebra and its Applications
*

We show that if the columns of A are ordered using

doi:10.1016/j.laa.2011.03.035
fatcat:h67li42jwrc6fohrxnrb2ugqzy
*minimum**degree*on A + A * , then*factoring*A using a sparse LU with partial pivoting algorithm generates only O(d max n) fill, requires only O(d max n ... We also propose an even more efficient*and*just-as-stable algorithm called sibling-*dominant*pivoting. ... This research was supported by an IBM Faculty Partnership Award, by grants 848/04*and*1045/09 from the Israel Science Foundation (founded by the Israel Academy of Sciences*and*Humanities),*and*by grant ...##
###
Approximation hardness of dominating set problems in bounded degree graphs

2008
*
Information and Computation
*

We study approximation hardness of the

doi:10.1016/j.ic.2008.07.003
fatcat:d76cljestneb3imw5fofypazca
*Minimum**Dominating*Set problem*and*its variants in undirected*and*directed graphs. ...*degree*graphs. ... Theorem 1 . 1*Minimum**Dominating*Set,*Minimum*Total*Dominating*Set,*and**Minimum*Connected*Dominating*Set cannot be approximated to within a*factor*of (1 − ε) ln n in polynomial time for any constant ε ...##
###
Distributed algorithms for edge dominating sets

2010
*
Proceeding of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing - PODC '10
*

Edge-based covering problems in port-numbering model 14 •

doi:10.1145/1835698.1835783
dblp:conf/podc/Suomela10
fatcat:ngv36ttsfnakfnnx5o5vlamg34
*Minimum*edge cover seems to be a bit too simple:*factor*2 approximation is trivial*and*tight• But what about*minimum*edge*dominating*sets? ... • Contribution: full characterisation of approximability of edge*dominating*sets in regular graphs*and*bounded-*degree*graphs Edge*dominating*sets: deterministic algorithms in port-numbering model ...##
###
Page 8949 of Mathematical Reviews Vol. , Issue 2003m
[page]

2003
*
Mathematical Reviews
*

C. (1-CLEM; Clemson, SC)

*Factor**domination**and**minimum**degree*. (English summary) Discrete Math. 262 (2003), no. 1-3, 113-119. ... We prove that in any graph of order n,*minimum**degree*6*and*maximum*degree*A#0, IR(G) <n/(1+6/A)*and*IR(G) — B(G) < ((A—2)/2A)n. The two bounds are attained by arbitrarily large graphs. ...##
###
On the number of components in 2-factors of claw-free graphs

2007
*
Discrete Mathematics
*

Additionally, we give a family of claw-free graphs with

doi:10.1016/j.disc.2006.11.022
fatcat:dzweix6apzgwjc4w46kcga2jh4
*minimum**degree*4 in which every 2-*factor*contains more than n/ components. ... In this paper, we prove that if a claw-free graph G with*minimum**degree*4 has no maximal clique of two vertices, then G has a 2-*factor*with at most (|G| − 1)/4 components. ... The edge-*degree*of an edge uv is defined as d(u) + d(v) − 2*and*the*minimum*edge-*degree*e (G) is the*minimum*number of the edge-*degrees*of all edges in G. ...##
###
Page 1494 of Mathematical Reviews Vol. , Issue 2001C
[page]

2001
*
Mathematical Reviews
*

A characterisation of connected graphs with

*minimum**degree*at least 2*and**domination*number exceeding a third their size is obtained. ... Connected graphs G of size q with*minimum**degree*at least 2 satisfying y,(G) > q/2 are characterised. ...##
###
Matching properties in connected domination critical graphs

2008
*
Discrete Mathematics
*

certain assumptions regarding connectivity

doi:10.1016/j.disc.2007.03.073
fatcat:hymsd66bqzfhtjtf5fzpz2tvr4
*and**minimum**degree*, a critical graph G with (ordinary)*domination*number 3 will be*factor*-critical (if |V (G)| is odd), bicritical (if |V (G)| is even) or 3- ... Plummer, 3-*factor*-criticality in*domination*critical graphs, Discrete Math. 2007, to appear [3].] on ordinary (i.e., not necessarily connected)*domination*, the first*and*third authors showed that under ... Note that the*minimum**degree*of the graph H 2n−6,2,2,2 is 3 for any n 4. 3-c-criticality*and**factor*-criticality In the case of odd graphs, the*minimum**degree*requirement necessary to guarantee*factor*-criticality ...##
###
On the Complexity of Making a Distinguished Vertex Minimum or Maximum Degree by Vertex Deletion
[article]

2014
*
arXiv
*
pre-print

Given a vertex weighted graph G=(V,E)

arXiv:1312.3779v3
fatcat:th5nmyqcqzhlte3hwmnyn4mhn4
*and*a specified, or "distinguished" vertex p ∈ V, MDD(min) is the problem of finding a*minimum*weight vertex set S ⊆ V∖{p} such that p becomes the*minimum**degree*vertex ... in G[V ∖ S];*and*MDD(max) is the problem of finding a*minimum*weight vertex set S ⊆ V∖{p} such that p becomes the maximum*degree*vertex in G[V ∖ S]. ... S ⊆ V is a*dominating*set in G if*and*only if p is the vertex of*minimum**degree*in H[V ′ \ S] (i.e. S is a solution to MDD(min) for H). Proof : Let S ⊆ V be a*dominating*set in G. ...
« Previous

*Showing results 1 — 15 out of 823,665 results*