离散数学
For an $n$-vertex graph $G$, let $z(G;k)$ denote the number of zero forcing sets of size $k$. A conjecture of Boyer et al. asserts that the path $P_n$ maximizes these numbers coefficientwise among all $n$-vertex graphs; equivalently, the…
Phylogenetic networks provide a framework for representing evolutionary histories involving reticulate events such as hybridization or horizontal gene transfer. A central problem is to infer such networks from local structural information.…
We prove that every class of Eulerian directed graphs of bounded carving width (equivalently of bounded degree and treewidth) is well-quasi-ordered by strong immersion. In fact, we prove a stronger result, namely that every class of…
Recent studies suggest that gradient-based methods applied to relaxed box-constrained Quadratic Unconstrained Binary Optimization (QUBO) formulations can outperform classical heuristics in some large-scale regimes, often relying on heavy…
We show that every proper minor-closed class of graphs admits a $(1+o(1))\log_2 n$-bit adjacency labelling scheme. Equivalently, for every proper minor-closed class $\mathcal{G}$ and every positive integer $n$ there exists an…
We study online scheduling to minimize total completion time with explorable uncertainty on single and multiple machines. Each job comes with an upper limit of its processing time, which could be potentially reduced by testing the job,…
Model counting is a fundamental problem that consists of determining the number of satisfying assignments for a given Boolean formula. The weighted variant, which computes the weighted sum of satisfying assignments, has extensive…
We study the problem of edge partitioning, where the goal is to partition the edge set of a graph into several parts. The replication factor of a vertex $v$ is the number of parts that contain edges incident to $v$. The goal is to minimize…
We study the sampling problem for simultaneous edge colorings. Given a pair of graphs $G_1=(V,E_1)$ and $G_2=(V,E_2)$ which are on the same vertex set $V$, a simultaneous edge coloring is an edge coloring of $G_1\cup G_2$ so that each of…
In the Flexible Graph Connectivity (FGC) problem, we are given an undirected multigraph on $n$ vertices with nonnegative edge costs, where each edge is classified as either safe or unsafe. Given integer parameters $p$ and $q$, the goal in…
Notions of graph similarity provide alternative perspective on the graph isomorphism problem and vice-versa. In this paper, we consider measures of similarity arising from mismatch norms as studied in Gervens and Grohe: the edit distance…
Catalan numbers and their interpretations in terms of Dyck paths are widely used in different topics of applied mathematics and computer science. Here, we consider a general approach for constrained Dyck paths. In particular, we study Dyck…
We study a colored generalization of the famous simple-switch Markov chain for sampling the set of graphs with a fixed degree sequence. Here we consider the space of graphs with colored vertices, in which we fix the degree sequence and…
Latin squares are $n\times n$ matrices containing $n$ symbols, where each symbol appears exactly once in each row and column. They were studied by Euler, later popularized through Sudoku, and remain a rich source of difficult combinatorial…
Arboreal networks are multi-rooted phylogenetic networks whose underlying graph is a tree. We give an encoding of stack-free arboreal networks in terms of triplets and the novel concept of a duet. This yields a polynomial time algorithm to…
In the permutation Mastermind game, the goal is to uncover a secret permutation $\sigma^\star \colon [n] \to [n]$ by making a series of guesses $\pi_1, \ldots, \pi_T$ which must also be permutations of $[n]$, and receiving as feedback after…
We propose a definition of graph subshifts of finite type that can be seen as extending both the notions of subshifts of finite type from classical symbolic dynamics and finitely presented groups from combinatorial group theory. These are…
In a recent work, we introduced a parametric framework for obtaining obstruction characterizations of graph parameters with respect to a quasi-ordering $\leqslant$ on graphs. Towards this, we proposed the concepts of class obstruction,…
We study solution discovery, where the goal is to obtain a feasible solution to a problem from an initial configuration by a bounded sequence of local moves. In many applications, however, the graph that defines which vertex sets are…
We introduce a fun problem that can be considered as a variant of the classic birthday problem, the Bottleneck Birthday Problem (BBP). It is stated as: what is the maximum number of people we have to choose so that no day of the year has…