A direct decomposition of 3-connected planar graphs.
A discontinuity in the distribution of fixed point sums.
A discrete Fourier kernel and Fraenkel's tiling conjecture
A Discretized Approach to W. T. Gowers' Game
We give an alternative proof of W. T. Gowers' theorem on block bases by reducing it to a discrete analogue on specific countable nets. We also give a Ramsey type result on k-tuples of block sequences in a normed linear space with a Schauder basis.
A distance between isomorphism classes of trees
A divisibility property of binomial coefficients viewed as an elementary sieve.
A dual proof of the upper bound conjecture for convex polytopes.
A duality based proof of the combinatorial nullstellensatz.
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 4-designs on 26 points
Using the Kramer-Mesner method, - designs with as a group of automorphisms and with in the set are constructed. The search uses specific partitioning of columns of the orbit incidence matrix, related to so-called “quasi-designs”. Actions of groups , and twisted are being compared. It is shown that there exist - designs with , respectively twisted as a group of automorphisms and with in the set . With in the set , there exist designs which possess all three considered groups...
A family of complete arcs in finite projective planes
A family of nonregular distance monotone graphs
A Family of Path Properties for Graphs.
A family of tridiagonal pairs related to the quantum affine algebra .
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 algorithm for MacMahon's partition analysis.
A fast multi-scale method for drawing large graphs.
A few more cyclic Steiner 2-designs.
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...