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Changing upper irredundance by edge addition

2003
*
Discrete Mathematics
*

Denote the

doi:10.1016/s0012-365x(02)00806-3
fatcat:dqbeynda2jemvmtoq5bs5jvjge
*upper**irredundance*number of a graph G*by*IR(G). A graph G is IR-*edge*-*addition*-sensitive if its*upper**irredundance*number*changes*whenever an*edge*of G is added to G. ... Research grants*by*the University, the South African National Research Foundation and NSERC (Canada) are gratefully acknowledged. ... Mynhardt was employed*by*the University of South Africa in the Department of Mathematics, Applied Mathematics and Astronomy, and E.J. Cockayne was visiting this department. ...##
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On the Complexity Landscape of the Domination Chain
[chapter]

2016
*
Lecture Notes in Computer Science
*

As this posed the majority of hitherto unsettled problems, we focus on

doi:10.1007/978-3-319-29221-2_6
fatcat:heoged57kvcupbz5fmah7qx6fq
*Upper**Irredundance*and Lower*Irredundance*that correspond to finding the largest*irredundant*set and resp. the smallest maximal*irredundant*... While Lower*Irredundance*is proved not c log(n)-approximable in polynomial time unless N P ⊆ DTIME(n log log n ), no such result is known for*Upper**Irredundance*. ... We gratefully acknowledge the support*by*the Deutsche Forschungsgemeinschaft, grant FE 560/6-1. 9 The current published records are held*by*the following two papers: J. Chen ...##
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Variable neighborhood search for extremal graphs. 22. Extending bounds for independence to upper irredundance

2009
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Discrete Applied Mathematics
*

The independence number α (resp.

doi:10.1016/j.dam.2009.04.004
fatcat:lbp76dv2vraq7n7y64tm2iefim
*upper**irredundance*number IR) is the maximum number of vertices of an independent (resp.*irredundant*) set of G. ... In previous work, a series of best possible lower and*upper*bounds on α and some other usual invariants of G were obtained*by*the system AGX 2, and proved either automatically or*by*hand. ... A set U is an*irredundant*set if for every u ∈ U, PN[u, U] = φ. The maximum cardinality of an*irredundant*set is called*upper**irredundance*number and denoted*by*IR. ...##
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Page 5485 of Mathematical Reviews Vol. , Issue 2002H
[page]

2002
*
Mathematical Reviews
*

Particular attention is given to the subclass of ir,(0)-graphs whose total

*irredundance*number either does not*change*(stable) or always*changes*(un- stable) under arbitrary single*edge**additions*. ... Let F) = K>V K3, Fs = K, V Ps and F; be obtained*by*identify- ing two adjacent*edges*of a K4 with an*edge*each of two different triangles. All these graphs and the cricket contain a claw. ...##
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Iterated colorings of graphs

2004
*
Discrete Mathematics
*

For a graph property P, in particular maximal independence, minimal domination and maximal

doi:10.1016/s0012-365x(03)00247-4
fatcat:eu25mnz6cndbdjraesdmq32sjq
*irredundance*, we introduce iterated P-colorings of graphs. ... The six graph parameters arising from either maximizing or minimizing the number of colors used for each property, are related*by*an inequality chain, and in this paper we initiate the study of these parameters ... Fig. 8 . 8 ir * (G) is reduced from 4 to 3*by*the*addition*of a new*edge*(see previous ÿgure). Fig. 9 . 9 Here we have reduced * (G) from 4 to 3*by*the*addition*of a new*edge*. ...##
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Introduction

1993
*
Discrete Applied Mathematics
*

The paper

doi:10.1016/0166-218x(93)90217-c
fatcat:iklvodekpnho3nyhvmz6acnvuy
*by*Golumbic and Laskar proves that this equality holds in circular arc graphs as well, and they go on to prove*additional*results on several variations of*irredundancy*on circular arc graphs ... The paper*by*Haynes, Brigham and Dutton looks at the extremal problem of determining the smallest number of*edges*required*by*a graph on n vertices having the property that removing an arbitrary set of ...##
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Breaking the 2n-barrier for Irredundance: Two lines of attack

2011
*
Journal of Discrete Algorithms
*

The lower and the

doi:10.1016/j.jda.2011.03.002
fatcat:txstt3rsnbbcdppraf4sqyxm6q
*upper**irredundance*numbers of a graph G, denoted ir(G) and IR(G), respectively, are conceptually linked to the domination and independence numbers and have numerous relations to other ... The second one is based, in*addition*, on a reduction to the Maximum Induced Matching problem providing a branch-and-reduce algorithm to solve it. ... The Co-MaxIR problem can be solved in time bounded*by*O (2.8752 k poly(n)). Using the win-win approach, the*upper**irredundance*number of a graph can be computed*by*an O * (1.9369 n ) time algorithm. ...##
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A polynomial-time fragment of dominance constraints

2000
*
Proceedings of the 38th Annual Meeting on Association for Computational Linguistics - ACL '00
*

This work was supported

doi:10.3115/1075218.1075265
dblp:conf/acl/KollerMN00
fatcat:7eyra7l7szhuzih5jcp32qd7e4
*by*the DFG in the SFB 378. ... If C is a directed cycle, we are done (see above); otherwise, the*edges*in C must*change*directions somewhere. ... We can assume without loss of generality that ϕ is*irredundant*; otherwise we make it*irredundant**by*removing dominance*edges*, which does not introduce new hypernormal cycles. ...##
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Avoidance colourings for small nonclassical Ramsey numbers

2011
*
Discrete Mathematics & Theoretical Computer Science
*

= n, respectively], where Gamma and IR denote respectively the

doi:10.46298/dmtcs.559
fatcat:koo3py74ifapbjj7odkcc44obu
*upper*domination number and the*irredundance*number of a graph. ... Graphs and Algorithms International audience The*irredundant*Ramsey number s - s(m, n) [*upper*domination Ramsey number u - u(m, n), respectively] is the smallest natural number s [u, respectively] such ... Computation of the parameter β(G) occurs exactly as in the case of IR(G), the only*change*being replacement of the requirement that S "is not*irredundant*" in Step 1 of Algorithm 1*by*the requirement that ...##
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Irredundant Buffer and Splitter Insertion and Scheduling-Based Optimization for AQFP Circuits
[article]

2021
*
arXiv
*
pre-print

In this paper, we develop (a) a linear-time algorithm to insert buffers and splitters irredundantly, and (b) optimization methods

arXiv:2109.00291v1
fatcat:ptytbcmqojfxzlezap6reg4fwm
*by*scheduling and*by*moving groups of gates, called chunks, together. ... Before technology mapping,*additional*buffer and splitter cells need to be inserted into AQFP circuits to fulfill two special constraints: (1) Input signals to a logic gate need to arrive at the same time ... Acknowledgments This work was supported in part*by*the EPFL Open Science Fund and*by*the SNF grant "Supercool: Design methods and tools for superconducting electronics", 200021_1920981. ...##
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A Survey of the Algorithmic Properties of Simplicial, Upper Bound and Middle Graphs

2006
*
Journal of Graph Algorithms and Applications
*

Three classes of graphs, simplicial,

doi:10.7155/jgaa.00123
fatcat:s7gzuht6onbvjb4emomuxmztx4
*upper*bound, and middle graphs, have been known for some time, but many of their algorithmic properties have not been published. ... Acknowledgments The first author would like to thank Steve Hedetniemi for first describing simplicial graphs to him, and to the Clemson Algorithms group for initial discussions of the simplicial and*upper*... Each of these must either use at least four distinct*edges*of T that have not been counted yet, or else use three*additional**edges*and connect to a non-direct path that uses at least five*additional**edges*...##
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A Parameterized Route to Exact Puzzles: Breaking the 2 n -Barrier for Irredundance
[chapter]

2010
*
Lecture Notes in Computer Science
*

The lower and the

doi:10.1007/978-3-642-13073-1_28
fatcat:qxiifrdksfbqle7blmkdwd7yc4
*upper**irredundance*numbers of a graph G, denoted ir(G) and IR(G) respectively, are conceptually linked to domination and independence numbers and have numerous relations to other graph ...*Additionally*, our work also appears to be the first example of a parameterized approach leading to a solution to a problem in exponential time algorithmics where the natural interpretation as an exact ...*Additionally*, for all v ∈ K i , we have N (v) ⊆ W. ...##
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Page 3577 of Mathematical Reviews Vol. , Issue 2004e
[page]

2004
*
Mathematical Reviews
*

M. (3-VCTR-MS; Victoria, BC)

*Changing**upper**irredundance**by**edge**addition*. (English summary) The 18th British Combinatorial Conference (Brighton, 2001). Discrete Math. 266 (2003), no. 1-3, 185-193. ... Summary: “Denote the*upper**irredundance*number of a graph G*by*IR(G). ...##
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Irredundance Graphs
[article]

2021
*
arXiv
*
pre-print

The

arXiv:1812.03382v3
fatcat:vcbht2ucwzgqtjre43c5eba3c4
*upper**irredundance*number IR(G) is the largest cardinality of an*irredundant*set of G; an IR(G)-set is an*irredundant*set of cardinality IR(G). ... A set D of vertices of a graph G=(V,E) is*irredundant*if each v of D satisfies (a) v is isolated in the subgraph induced*by*D, or (b) v is adjacent to a vertex in V-D that is nonadjacent to all other vertices ... We study the*upper**irredundance*graph (IR-graph for short) of a given graph G -the ways in which maximum*irredundant*sets (defined below) of G can be reconfigured successively into other such sets*by*exchanging ...##
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Page 1681 of Mathematical Reviews Vol. , Issue 2000c
[page]

2000
*
Mathematical Reviews
*

Summary: “Let G = (VE) be a graph and £, T and IR its independence,

*upper*domination and*upper**irredundance*number, respectively. ... Then the result is applied to study how the Laplacian spectrum of a graph*changes*when adding an*edge*.” 2000c:05105 05C62 05C85 Kratsch, Dieter (D-FSUMI; Jena); Rampon, Jean-Xavier (F-NANTC-IR; Nantes) ...
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