### Recent Submissions

• #### Showing non-realizability of spheres by distilling a tree ﻿

(2021)
Conference report
Open Access
In [Zhe20a], Hailun Zheng constructs a combinatorial 3-sphere on 16 vertices whose graph is the complete 4-partite graph K4;4;4;4. Such a sphere seems unlikely to be realizable as the boundary complex of a 4-dimensional ...
• #### Polynomials for marked graphs and the chromatic symmetric function ﻿

Conference lecture
Restricted access - publisher's policy
• #### Weak components of the directed configuration model ﻿

(Springer, 2021)
Conference report
Open Access
We study the threshold for the existence of a linear order weakly connected component in the directed configuration model, confirming analytic but non-rigorous results recently obtained by Kryven [8]. We also establish ...
• #### On list k-coloring convex bipartite graphs ﻿

(Springer, 2020)
Conference report
Open Access
List k–Coloring (LI k-COL) is the decision problem asking if a given graph admits a proper coloring compatible with a given list assignment to its vertices with colors in {1,2,..., k}. The problem is known to be NP-hard ...
• #### How to determine if a random graph with a fixed degree sequence has a giant component ﻿

(Institute of Electrical and Electronics Engineers (IEEE), 2016)
Conference report
Open Access
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 ...
• #### Improved bounds for randomly sampling colorings via linear programming ﻿

(2019)
Conference report
Restricted access - publisher's policy
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)
Conference report
Open Access
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 ...
• #### On zero-one and convergence laws for graphs embeddable on a fixed surface ﻿

(Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018)
Conference report
Open Access
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 ...
• #### Maximal independent sets and maximal matchings in series-parallel and related graph classes ﻿

(Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018)
Conference lecture
Open Access
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 ...
• #### Graph classes with given 3-connected components: asymptotic counting, limit laws and critical phenomena ﻿

(Edicions de la Universitat de Lleida (UdL), 2008)
Conference lecture
Restricted access - publisher's policy
Consider a family T of 3-connected graphs, and let G be the class of graphs whose 3-connected components are graphs in T . We present a general framework for analyzing such graphs classes based on singularity analysis of ...