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
On price of symmetrisation
[article]
2013
arXiv
pre-print
Preserved Fulltext
Acknowledgements The authors would like to thank Alain Hertz, Gilles Caporossi and Hadrien Lepousé for useful discussions about Conjecture 9. ...
arXiv:1310.2775v1
fatcat:vz2bkevr4bcejb5kl5tjlxacme
PHOEG Helps Obtaining Extremal Graphs
[article]
2017
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
In 2008, Mélot presented GraPHedron [7] . This tool differs from the previous ones by its ideas. ...
arXiv:1712.07861v1
fatcat:lfyueokggzhytlieq6kgspoqie
Fibonacci Index and Stability Number of Graphs: a Polyhedral Study
[article]
2008
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
The Fibonacci index of a graph is the number of its stable sets. This parameter is widely studied and has applications in chemical graph theory. In this paper, we establish tight upper bounds for the Fibonacci index in terms of the stability number and the order of general graphs and connected graphs. Turán graphs frequently appear in extremal graph theory. We show that Turán graphs and a connected variant of them are also extremal for these particular problems. We also make a polyhedral study
arXiv:0811.1449v1
fatcat:6npw4h6tfzhqxoeluesdm73f6e
more »
... y establishing all the optimal linear inequalities for the stability number and the Fibonacci index, inside the classes of general and connected graphs of order n.
Digenes: genetic algorithms to discover conjectures about directed and undirected graphs
[article]
2013
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Moreover, Hansen and Mélot [26] proved that irregularity is maximal if and only if Table 1 denotes statistics regarding these three problems. ...
arXiv:1304.7993v1
fatcat:bxifiewz4jaz3lzxrkis3i3ire
The average size of maximal matchings in graphs
[article]
2022
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
We investigate the ratio I(G) of the average size of a maximal matching to the size of a maximum matching in a graph G. If many maximal matchings have a size close to μ(G), this graph invariant has a value close to 1. Conversely, if many maximal matchings have a small size, I(G) approaches 1/2. We propose a general technique to determine the asymptotic behavior of (G) for various classes of graphs. To illustrate the use of this technique, we first show how it makes it possible to find known
arXiv:2204.10236v1
fatcat:ez5kb4swzfa5jdoneqairqzs5q
more »
... ptotic values of I(G) which were typically obtained using generating functions, and we then determine the asymptotic value of I(G) for other families of graphs, highlighting the spectrum of possible values of this graph invariant between 1/2 and 1.
Maximum Eccentric Connectivity Index for Graphs with Given Diameter
[article]
2018
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
The eccentricity of a vertex v in a graph G is the maximum distance between v and any other vertex of G. The diameter of a graph G is the maximum eccentricity of a vertex in G. The eccentric connectivity index of a connected graph is the sum over all vertices of the product between eccentricity and degree. Given two integers n and D with D≤ n-1, we characterize those graphs which have the largest eccentric connectivity index among all connected graphs of order n and diameter D. As a corollary,
arXiv:1808.10203v1
fatcat:zsdu7vuvnrca3jptggq4f5gbia
more »
... e also characterize those graphs which have the largest eccentric connectivity index among all connected graphs of a given order n.
Integral complete split graphs
2002
Publikacija Elektrotehnickog fakulteta - serija matematika
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
We give characterizations of integral graphs in the family of complete split graphs and a few related families of graphs.
doi:10.2298/petf0213089h
fatcat:5kehyk6hyrafhdz2jwburpnfgy
Facet defining inequalities among graph invariants: The system GraPHedron
2008
Discrete Applied Mathematics
Preserved Fulltext
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.
We present a new computer system, called GraPHedron, which uses a polyhedral approach to help the user to discover optimal conjectures in graph theory. We define what should be optimal conjectures and propose a formal framework allowing to identify them. Here, graphs with n nodes are viewed as points in the Euclidian space, whose coordinates are the values of a set of graph invariants. To the convex hull of these points corresponds a finite set of linear inequalities. These inequalities
doi:10.1016/j.dam.2007.09.005
fatcat:z4m6o7vydbhxrjhhfylgn2e2i4
more »
... for a few values of n can be possibly generalized automatically or interactively. They serve as conjectures which can be considered as optimal by geometrical arguments. We describe how the system works, and all optimal relations between the diameter and the number of edges of connected graphs are given, as an illustration. Other applications and results are mentioned, and the forms of the conjectures that can be currently obtained with GraPHedron are characterized.
Computers and discovery in algebraic graph theory
2002
Linear Algebra and its Applications
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
We survey computers systems which help to obtain and sometimes provide automatically conjectures and refutations in algebraic graph theory. Résumé On passe en revue les systèmes informatiques qui aident à obtenir et parfois donnent automatiquement des conjectures et réfutations en théorie algébrique des graphes.
doi:10.1016/s0024-3795(02)00386-5
fatcat:qxtwo74ygra5la6vj2fpscn2mq
Counting the number of non-equivalent vertex colorings of a graph
2016
Discrete Applied Mathematics
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
We study the number P(G) of non-equivalent ways of coloring a given graph G, also known as the (graphical) Bell number of G. We show some similarities and differences between this graph invariant and the well known chromatic polynomial. We then relate P(G) to Stirling numbers of the second kind, and to Bell, Fibonacci, and Lucas numbers, by computing the values of this invariant for some families of graphs. We finally study upper and lower bounds on P(G) for graphs with fixed maximum degree.
doi:10.1016/j.dam.2015.09.015
fatcat:pbp5qasvsjagpm4rd5j6v4bagu
A Tight Analysis of the Maximal Matching Heuristic
[chapter]
2005
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2007; you can also visit the original URL.
The file type is application/pdf.
We study the algorithm that iteratively removes adjacent vertices from a simple, undirected graph until no edge remains. This algorithm is a well-known 2-approximation to three classical NP-hard optimization problems: MINIMUM VERTEX COVER, MINIMUM MAXIMAL MATCHING and MINIMUM EDGE DOMINATING SET. We show that the worst-case approximation factor of this simple method can be expressed in a finer way when assumptions on the density of the graph is made. For graphs with an average degree at least
doi:10.1007/11533719_71
fatcat:jch3ymqmgjaplhgfzjxwnaxba4
more »
... called weakly -dense graphs, we show that the asymptotic approximation factor is min{2, 1/(1 − √ 1 − )}. For graphs with a minimum degree at least n -strongly -dense graphs -we show that the asymptotic approximation factor is min{2, 1/ }. These bounds are obtained through a careful analysis of the tight examples. Chercheur qualifié du F.N.R.S. Corresponding author.
Minimum Eccentric Connectivity Index for Graphs with Fixed Order and Fixed Number of Pending Vertices
[article]
2018
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
The eccentric connectivity index of a connected graph G is the sum over all vertices v of the product d_G(v) e_G(v), where d_G(v) is the degree of v in G and e_G(v) is the maximum distance between v and any other vertex of G. This index is helpful for the prediction of biological activities of diverse nature, a molecule being modeled as a graph where atoms are represented by vertices and chemical bonds by edges. We characterize those graphs which have the smallest eccentric connectivity index
arXiv:1809.03158v1
fatcat:ytw5foyuy5dend2a4vzskgfuye
more »
... ong all connected graphs of a given order n. Also, given two integers n and p with p≤ n-1, we characterize those graphs which have the smallest eccentric connectivity index among all connected graphs of order n with p pending vertices.
Fibonacci index and stability number of graphs: a polyhedral study
2009
Journal of combinatorial optimization
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
The Fibonacci index of a graph is the number of its stable sets. This parameter is widely studied and has applications in chemical graph theory. In this paper, we establish tight upper bounds for the Fibonacci index in terms of the stability number and the order of general graphs and connected graphs. Turán graphs frequently appear in extremal graph theory. We show that Turán graphs and a connected variant of them are also extremal for these particular problems. We also make a polyhedral study
doi:10.1007/s10878-009-9228-7
fatcat:mzfdrb3i3zbdfei2exegfxbnpm
more »
... y establishing all the optimal linear inequalities for the stability number and the Fibonacci index, inside the classes of general and connected graphs of order n.
Using Graph Theory to Derive Inequalities for the Bell Numbers
[article]
2021
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf.
Other Versions
The Bell numbers count the number of different ways to partition a set of n elements while the graphical Bell numbers count the number of non-equivalent partitions of the vertex set of a graph into stable sets. This relation between graph theory and integer sequences has motivated us to study properties on the average number of colors in the non-equivalent colorings of a graph to discover new non trivial inequalities for the Bell numbers. Example are given to illustrate our approach.
arXiv:2104.00552v2
fatcat:k3vizauhqzgmxmvyibghef472y
Upper bounds on the average number of colors in the non-equivalent colorings of a graph
[article]
2021
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf.
A coloring of a graph is an assignment of colors to its vertices such that adjacent vertices have different colors. Two colorings are equivalent if they induce the same partition of the vertex set into color classes. Let 𝒜(G) be the average number of colors in the non-equivalent colorings of a graph G. We give a general upper bound on 𝒜(G) that is valid for all graphs G and a more precise one for graphs G of order n and maximum degree Δ(G)∈{1,2,n-2}.
arXiv:2105.01120v1
fatcat:5umi6mmjxnfunmxa67t3ejj4uu
« Previous
Showing results 1 — 15 out of 41 results