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Big Ramsey degrees of 3-uniform hypergraphs
(2019)
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Given a countably infinite hypergraph $\mathcal R$ and a finite hypergraph $\mathcal A$, the \emph{big Ramsey degree} of $\mathcal A$ in $\mathcal R$ isthe least number $L$ such that, for every finite $k$ and every ...
On zero-one and convergence laws for graphs embeddable on a fixed surface
(Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018)
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We show that for no surface except for the plane does monadic second-order logic (MSO) have a zero-one-law - and not even a convergence law - on the class of (connected) graphs embeddable on the surface. In addition we ...
Improved bounds for randomly sampling colorings via linear programming
(2019)
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Accés restringit per política de l'editorial
Text en actes de congrés.
Accés restringit per política de l'editorial
A well-known conjecture in computer science and statistical physics is that Glauber dynamics on the set of k-colorings of a graph G on n vertices with maximum degree ¿ is rapidly mixing for k = ¿ + 2. In FOCS 1999, Vigoda ...
Set systems with distinct sumsets
(Elsevier, 2018)
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Text en actes de congrés.
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A family $\mathcal{A}$ of $k$-subsets of $\{1,2,\dots, N\}$ is a Sidon system if the sumsets $A+A'$, $A,A'\in \mathcal{A}$ are pairwise distinct.
We show that the largest cardinality $F_k(N)$ of a Sidon system of $k$-subsets ...
The canonical Tutte polynomial for signed graphs
(2019)
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We construct a new polynomial invariant for signed graphs, the trivariate Tutte polynomial, which contains among its evaluations the number of proper colorings and the number of nowhere-zero flows. In this, it parallels ...
How to determine if a random graph with a fixed degree sequence has a giant component
(Institute of Electrical and Electronics Engineers (IEEE), 2016)
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The traditional Erdos-Renyi model of a random network is of little use in modelling the type of complex networks which modern researchers study. In this graph, every pair of vertices is equally likely to be connected by ...
Maximal independent sets and maximal matchings in series-parallel and related graph classes
(Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018)
Comunicació de congrés.
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Comunicació de congrés.
Accés obert
We provide combinatorial decompositions as well as asymptotic tight estimates for two maximal parameters: the number and average size of maximal independent sets and maximal matchings in seriesparallel graphs (and related ...
Extremal families for Kruskal-Katona Theorem
(2019)
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Text en actes de congrés.
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Given a set of size $n$ and a positive integer $k<n$, Kruskal--Katona theorem gives the minimum size of the shadow of a family $S$ of $k$-sets of $[n]$ in terms of the cardinality of $S$. We give a characterization of the ...