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On the number of labeled graphs of bounded treewidth
(2018-06-01)
Article
Open AccessLet be Tnk the number of labeled graphs on vertices and treewidth at most (equivalently, the number o<f labeled partial -trees). We show that [...] for k>1 and some explicit absolute constant c>0. Disregarding terms depending ... -
Transformation and decomposition of clutters into matroids
(2017-05-25)
Article
Open AccessA clutter is a family of mutually incomparable sets. The set of circuits of a matroid, its set of bases, and its set of hyperplanes are examples of clutters arising from matroids. In this paper we address the question of ... -
On trees with the same restricted U-polynomial and the Prouhet–Tarry–Escott problem
(2017-06)
Article
Open AccessThis paper focuses on the well-known problem due to Stanley of whether two non-isomorphic trees can have the same U-polynomial (or, equivalently, the same chromatic symmetric function). We consider the Uk-polynomial, which ... -
Threshold functions and Poisson convergence for systems of equations in random sets
(2017-05-10)
Article
Open AccessWe study threshold functions for the existence of solutions to linear systems of equations in random sets and present a unified framework which includes arithmetic progressions, sum-free sets, Bh[g]Bh[g]-sets and Hilbert ... -
Corrigendum to"On the limiting distribution of the metric dimension for random forests" [European J. Combin. 49 (2015) 68-89]
(2017-07-22)
Article
Open AccessIn the paper ”On the limiting distribution of the metric dimension for random forests” the metric dimension ß(G) of sparse G(n, p) with p = c/n and c < 1 was studied (Theorem 1.2). In the proof of this theorem, for the ... -
Counting configuration-free sets in groups
(2017-01-01)
Article
Open Access© 2017 Elsevier Ltd. We provide asymptotic counting for the number of subsets of given size which are free of certain configurations in finite groups. Applications include sets without solutions to equations in non-abelian ... -
Random strategies are nearly optimal for generalized van der Waerden Games
(2017-08-01)
Article
Open AccessIn a (1 : q) Maker-Breaker game, one of the central questions is to find (or at least estimate) the maximal value of q that allows Maker to win the game. Based on the ideas of Bednarska and Luczak [Bednarska, M., and T. ... -
Enumeration of labeled 4-regular planar graphs
(2017-08-01)
Article
Open AccessIn this extended abstract, we present the first combinatorial scheme for counting labeled 4-regular planar graphs through a complete recursive decomposition. More precisely, we show that the exponential generating function ... -
Counting outerplanar maps
(2017-04-13)
Article
Open AccessA map is outerplanar if all its vertices lie in the outer face. We enumerate various classes of rooted outerplanar maps with respect to the number of edges and vertices. The proofs involve several bijections with lattice ... -
Subgraph statistics in subcritical graph classes
(2017-04-01)
Article
Open AccessLet H be a fixed graph and math formula a subcritical graph class. In this paper we show that the number of occurrences of H (as a subgraph) in a graph in math formula of order n, chosen uniformly at random, follows a ... -
A lower bound for the size of a Minkowski sum of dilates
(2011-03-01)
Article
Open AccessLet A be a finite non-empty set of integers. An asymptotic estimate of the size of the sum of several dilates was obtained by Bukh. The unique known exact bound concerns the sum |A + k·A|, where k is a prime and |A| is ... -
Asymptotic enumeration of non-crossing partitions on surfaces
(2013-03-01)
Article
Open AccessWe generalize the notion of non-crossing partition on a disk to general surfaces with boundary. For this, we consider a surface S and introduce the number CS(n) of noncrossing partitions of a set of n points laying on the ...
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