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An integer program and new lower bounds for computing the strong rainbow connection numbers of graphs
[article]
2021
arXiv
pre-print
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We present an integer programming model to compute the strong rainbow connection number, src(G), of any simple graph G. ...
We demonstrate the efficacy of our methods by computing the strong rainbow connection numbers of graphs containing up to 379 vertices. ...
The authors would like to thank Zachary Kingston of Rice University for helpful comments and conversations. ...
arXiv:2006.02988v2
fatcat:u4aknsbzgfebfebvmshyhafi24
Total $k$-rainbow domination subdivision number in graphs
2020
Computer Science Journal of Moldova
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In this paper, we initiate the study of total $k$-rainbow domination subdivision number in graphs and we present sharp bounds for ${\rm sd}_{\gamma_{trk}}(G)$. ...
In addition, we determine the total 2-rainbow domination subdivision number of complete bipartite graphs and show that the total 2-rainbow domination subdivision number can be arbitrary large. ...
[2] showed that for any connected graph G of order n ≥ 3, γ trk (G) ≥ ⌈ kn ∆(G)+k−1 ⌉. Applying this lower bound and Corollary 8, the next result follows. Corollary 9. ...
doaj:da5600cafd7c4e65bda4e761d81180c3
fatcat:omfptjc6mnedfj3mprh5m3btca
Multicolour paths in graphs: NP-hardness, algorithms, and applications on routing in WDM networks
2016
Journal of combinatorial optimization
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Additionally, we develop Branch and Bound algorithms, ILPs, and heuristics for the problem. We then perform an experimental analysis of the developed algorithms to compare their performances. ...
Let G = (V, E) be a (directed) graph with a set of nodes V and a set of edges E in which each edge has an associated positive weight w(i, j), and let C = {1, 2, . . . , x} be a set of x colours, x ∈ N. ...
Denoted by src(G), the strong rainbow connectivity number of a graph is the minimum number of colours needed to make a graph G strongly rainbow connected. ...
doi:10.1007/s10878-016-0003-2
fatcat:dbkuesrlbbhb3mnhrc425bypmm
Super efficiency of efficient geodesics in the complex of curves
[article]
2021
arXiv
pre-print
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The proof relies on a new intersection growth inequality between intersection number of curves and their distance in the complex of curves, together with a thorough analysis of the dot graph associated ...
and the second author (see arXiv:1408.4133) that there is an explicitly computable list of at most d^(6g-6) candidates for the v_1 vertex. ...
In section 2, we utilize the intersection number of a minimal filling pair as a lower bound and linear integer programming to establish the growth rate to prove Theorem 1.3. ...
arXiv:2008.09665v2
fatcat:cxe3sp75qbckpc7uvecgtemd6e
Minimum color‐degree perfect b ‐matchings
2020
Networks
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The last speaker of the session will chair the session, with two exceptions for PhD-only sessions: Combinatorial Optimization (Mon 18, Room PP, 16-17) chaired by R. ...
Schedule The seminar rooms are the Paul Painlevé (PP), the Robert Faure (Z) and the Jean-Baptiste Say (Y) amphitheatres, located in Access 1, lower ground floor. ...
Remarks We presented a new view of Gomory pure and mixed-integer cuts, aimed at incorporating in the familiar column-generation paradigm, employing the primal simplex algorithm. ...
doi:10.1002/net.21974
fatcat:4qgtutmxrrcy7anvxks4fivcii
The b-Chromatic Number of Cubic Graphs
2010
Graphs and Combinatorics
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We will also report about the status of this problem for graphs with minimum degree at least four. Keywords: Rainbow colouring, rainbow connectivity, extremal problem. ...
Laborde, Payan and Xuong [1] conjectured that every digraph has an independent set of vertices that meets every longest path. We consider the conjecture for special classes of oriented graphs. ...
New lower bounds on the independence number of a graph in terms of order, size, and clique number are presented. ...
doi:10.1007/s00373-010-0898-9
fatcat:5j4t3ji33bbopoker7veh5aybi
Refuting conjectures in extremal combinatorics via linear programming
[article]
2019
arXiv
pre-print
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We apply simple linear programming methods and an LP solver to refute a number of open conjectures in extremal combinatorics. ...
Acknowledgement: The author is indebted to Bernard Lidický who introduced him to linear programming. ...
an Integer Program (IP) 1 . ...
arXiv:1903.05495v1
fatcat:iuegd3t2krhebhypkvtz7dqy7i
Topological and Geometric Combinatorics
2011
Oberwolfach Reports
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We also conjecture a new lower bound on the number of vertices of an even dimensional triangulated manifold in terms of its dimension, connectivity and Euler characteristic. ...
Some other applications include lower bounds for the connectivity of independence complexes, in particular of claw-free graphs and therefore of matching complexes. ...
An easy and well-known reduction shows that one need only consider the case where n is a squarefree product of primes. ...
doi:10.4171/owr/2011/08
fatcat:kcwryms27fecjjs4hciq6ixa2q
When Maximum Stable Set can be solved in FPT time
[article]
2019
arXiv
pre-print
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In this paper, we introduce some variants of co-graphs with parameterized noise, that is, graphs that can be made into disjoint unions or complete sums by the removal of a certain number of vertices and ...
the addition/deletion of a certain number of edges per incident vertex, both controlled by the parameter. ...
Ramsey numbers For two positive integers a and b, R(a, b) is the smallest integer such that any graph with at least that many vertices has an independent set of size a or a clique of size b. ...
arXiv:1909.08426v1
fatcat:zejkso7etzgh5c4qemvfwvfpbm
Algebra in Computational Complexity (Dagstuhl Seminar 14391)
2015
Dagstuhl Reports
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NP and circuit lower bounds, the effort to resolve the complexity of matrix multiplication, and a framework for constructing locally testable codes. ...
The Razborov-Smolensky polynomial-approximation method for proving constantdepth circuit lower bounds, the PCP characterization of NP, and the Agrawal-Kayal-Saxena polynomial-time primality test are some ...
the number of integer roots of a univariate polynomial should be polynomially bounded in the size of the smallest straight-line program computing it. ...
doi:10.4230/dagrep.4.9.85
dblp:journals/dagstuhl-reports/AgrawalKTU14
fatcat:iailudx2rrhaxenbi3d7ou73ly
Ramsey Theory in the Work of Paul Erdős
[chapter]
2013
The Mathematics of Paul Erdős II
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, in theoretical computer science for lower bounds for various measures of complexity. ...
For example, the search for an explicit graph of size say 2 n=2 which w ould demonstrate this Ramsey lower bound has been so far unsuccessful. ...
doi:10.1007/978-1-4614-7254-4_13
fatcat:vqvyhfhj3ngr7c3vokrsmrt2ai
Ramsey Theory in the Work of Paul Erdős
[chapter]
1997
Algorithms and Combinatorics
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, in theoretical computer science for lower bounds for various measures of complexity. ...
For example, the search for an explicit graph of size say 2 n=2 which w ould demonstrate this Ramsey lower bound has been so far unsuccessful. ...
doi:10.1007/978-3-642-60406-5_16
fatcat:cqkc3inzjfe4lbu2jj4oem2fv4
Integrality gaps for colorful matchings
2019
Discrete Optimization
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2018 pre-print arXiv:1801.07937v2 fatcat:64q5p5fbz5fzjj43qvy2xon5nmOther Versions
We study the integrality gap of the natural linear programming relaxation for the Bounded Color Matching (BCM) problem. ...
We provide several families of instances and establish lower bounds on their integrality gaps and we study how the Sherali-Adams "lift-and-project" technique behaves on these instances. ...
E k ) be an instance of this rainbow matching problem. For each color class C j , create a new vertex c j and let N be the set of all these new vertices. ...
doi:10.1016/j.disopt.2018.12.003
fatcat:64jqlwfopjfrxi4dczlirzqxma
Mathematical and Algorithmic Analysis of Network and Biological Data
[article]
2014
arXiv
pre-print
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This dissertation contributes to mathematical and algorithmic problems that arise in the analysis of network and biological data. ...
The rainbow connectivity rc(G) of a connected graph G is the smallest number of colors that are needed in order to make G rainbow edge connected. ...
Furthermore, we use random graphs to perform an average case analysis for rainbow connectivity, an intriguing connectivity concept. ...
arXiv:1407.0375v1
fatcat:6s2qka5fazbl7bzxz4k3u75hzm
Multicolor and directed edit distance
2011
Journal of Combinatorics
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The theory for computing the edit distance is extended using random structures and so-called types or colored homomorphisms of graphs. ...
In this paper, a generalization of graph editing is considered for multicolorings of the complete graph as well as for directed graphs. ...
Let H be a hereditary property of digraphs and P a palette. Fix a density vector with respect to P, p = (p, q). The limit dist(p, H) := lim n→∞ dist n (p, H) exists. Moreover, ...
doi:10.4310/joc.2011.v2.n4.a4
fatcat:j4torni2jvhdxduki6xtawk2ke
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