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Changing upper irredundance by edge addition

E.J Cockayne, O Favaron, W Goddard, P.J.P Grobler, C.M Mynhardt
2003 Discrete Mathematics  
Denote the 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.  ... 
doi:10.1016/s0012-365x(02)00806-3 fatcat:dqbeynda2jemvmtoq5bs5jvjge

On the Complexity Landscape of the Domination Chain [chapter]

Cristina Bazgan, Ljiljana Brankovic, Katrin Casel, Henning Fernau
2016 Lecture Notes in Computer Science  
As this posed the majority of hitherto unsettled problems, we focus on 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  ... 
doi:10.1007/978-3-319-29221-2_6 fatcat:heoged57kvcupbz5fmah7qx6fq

Variable neighborhood search for extremal graphs. 22. Extending bounds for independence to upper irredundance

Mustapha Aouchiche, Odile Favaron, Pierre Hansen
2009 Discrete Applied Mathematics  
The independence number α (resp. 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.  ... 
doi:10.1016/j.dam.2009.04.004 fatcat:lbp76dv2vraq7n7y64tm2iefim

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.  ... 

Iterated colorings of graphs

Sandra M Hedetniemi, Stephen T Hedetniemi, Alice A McRae, Dee Parks, Jan Arne Telle
2004 Discrete Mathematics  
For a graph property P, in particular maximal independence, minimal domination and maximal 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.  ... 
doi:10.1016/s0012-365x(03)00247-4 fatcat:eu25mnz6cndbdjraesdmq32sjq

Introduction

MartinCharles Golumbic, Renu Laskar
1993 Discrete Applied Mathematics  
The paper 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  ... 
doi:10.1016/0166-218x(93)90217-c fatcat:iklvodekpnho3nyhvmz6acnvuy

Breaking the 2n-barrier for Irredundance: Two lines of attack

Daniel Binkele-Raible, Ljiljana Brankovic, Marek Cygan, Henning Fernau, Joachim Kneis, Dieter Kratsch, Alexander Langer, Mathieu Liedloff, Marcin Pilipczuk, Peter Rossmanith, Jakub Onufry Wojtaszczyk
2011 Journal of Discrete Algorithms  
The lower and the 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.  ... 
doi:10.1016/j.jda.2011.03.002 fatcat:txstt3rsnbbcdppraf4sqyxm6q

A polynomial-time fragment of dominance constraints

Alexander Koller, Kurt Mehlhorn, Joachim Niehren
2000 Proceedings of the 38th Annual Meeting on Association for Computational Linguistics - ACL '00  
This work was supported 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.  ... 
doi:10.3115/1075218.1075265 dblp:conf/acl/KollerMN00 fatcat:7eyra7l7szhuzih5jcp32qd7e4

Avoidance colourings for small nonclassical Ramsey numbers

Alewyn Petrus Burger, Jan H. Vuuren
2011 Discrete Mathematics & Theoretical Computer Science  
= n, respectively], where Gamma and IR denote respectively the 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  ... 
doi:10.46298/dmtcs.559 fatcat:koo3py74ifapbjj7odkcc44obu

Irredundant Buffer and Splitter Insertion and Scheduling-Based Optimization for AQFP Circuits [article]

Siang-Yun Lee, Heinz Riener, Giovanni De Micheli
2021 arXiv   pre-print
In this paper, we develop (a) a linear-time algorithm to insert buffers and splitters irredundantly, and (b) optimization methods 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.  ... 
arXiv:2109.00291v1 fatcat:ptytbcmqojfxzlezap6reg4fwm

A Survey of the Algorithmic Properties of Simplicial, Upper Bound and Middle Graphs

Grant A. Cheston, Tjoen Seng Jap
2006 Journal of Graph Algorithms and Applications  
Three classes of graphs, simplicial, 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  ... 
doi:10.7155/jgaa.00123 fatcat:s7gzuht6onbvjb4emomuxmztx4

A Parameterized Route to Exact Puzzles: Breaking the 2 n -Barrier for Irredundance [chapter]

Daniel Binkele-Raible, Ljiljana Brankovic, Henning Fernau, Joachim Kneis, Dieter Kratsch, Alexander Langer, Mathieu Liedloff, Peter Rossmanith
2010 Lecture Notes in Computer Science  
The lower and the 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.  ... 
doi:10.1007/978-3-642-13073-1_28 fatcat:qxiifrdksfbqle7blmkdwd7yc4

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).  ... 

Irredundance Graphs [article]

Kieka Mynhardt, Riana Roux
2021 arXiv   pre-print
The 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  ... 
arXiv:1812.03382v3 fatcat:vcbht2ucwzgqtjre43c5eba3c4

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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