A deletion game on graphs: “Le Pic Arête".
A density result for random sparse oriented graphs and its relation to a conjecture of Woodall.
A Different Short Proof of Brooks’ Theorem
Lovász gave a short proof of Brooks’ theorem by coloring greedily in a good order. We give a different short proof by reducing to the cubic case.
A Digrapf Approach to the Edge-Reconstruction Conjecture
A digraph equation for homomorphic images.
A direct decomposition of 3-connected planar graphs.
A distance between isomorphism classes of trees
A dual proof of the upper bound conjecture for convex polytopes.
A factor graph based genetic algorithm
We propose a new linkage learning genetic algorithm called the Factor Graph based Genetic Algorithm (FGGA). In the FGGA, a factor graph is used to encode the underlying dependencies between variables of the problem. In order to learn the factor graph from a population of potential solutions, a symmetric non-negative matrix factorization is employed to factorize the matrix of pair-wise dependencies. To show the performance of the FGGA, encouraging experimental results on different separable problems...
A family of nonregular distance monotone graphs
A Family of Path Properties for Graphs.
A Fan-Type Heavy Pair Of Subgraphs For Pancyclicity Of 2-Connected Graphs
Let G be a graph on n vertices and let H be a given graph. We say that G is pancyclic, if it contains cycles of all lengths from 3 up to n, and that it is H-f1-heavy, if for every induced subgraph K of G isomorphic to H and every two vertices u, v ∈ V (K), dK(u, v) = 2 implies [...] mindG(u),dG(v)≥n+12 . In this paper we prove that every 2-connected K1,3, P5-f1-heavy graph is pancyclic. This result completes the answer to the problem of finding f1-heavy pairs of subgraphs implying pancyclicity...
A fast multi-scale method for drawing large graphs.
A few remarks on the history of MST-problem
On the background of Borůvka’s pioneering work we present a survey of the development related to the Minimum Spanning Tree Problem. We also complement the historical paper Graham-Hell [GH] by a few remarks and provide an update of the extensive literature devoted to this problem.
A Fiedler-like theory for the perturbed Laplacian
The perturbed Laplacian matrix of a graph is defined as , where is any diagonal matrix and is a weighted adjacency matrix of . We develop a Fiedler-like theory for this matrix, leading to results that are of the same type as those obtained with the algebraic connectivity of a graph. We show a monotonicity theorem for the harmonic eigenfunction corresponding to the second smallest eigenvalue of the perturbed Laplacian matrix over the points of articulation of a graph. Furthermore, we use...
A Finite Characterization and Recognition of Intersection Graphs of Hypergraphs with Rank at Most 3 and Multiplicity at Most 2 in the Class of Threshold Graphs
We characterize the class [...] L32 of intersection graphs of hypergraphs with rank at most 3 and multiplicity at most 2 by means of a finite list of forbidden induced subgraphs in the class of threshold graphs. We also give an O(n)-time algorithm for the recognition of graphs from [...] L32 in the class of threshold graphs, where n is the number of vertices of a tested graph.
A forbidden subgraphs characterization and a polynomial algorithm for randomly decomposable graphs
A formula for all minors of the adjacency matrix and an application
We supply a combinatorial description of any minor of the adjacency matrix of a graph. This description is then used to give a formula for the determinant and inverse of the adjacency matrix, A(G), of a graph G, whenever A(G) is invertible, where G is formed by replacing the edges of a tree by path bundles.
A formula for the bivariate map asymptotics constants in terms of the univariate map asymptotics constants.
A further application of matrix analysis to communication structure in oceanic anthropology