Related papers: Unique perfect matchings, forbidden transitions an…
This note presents several results in graph theory inspired by the author's work in the proof theory of linear logic; these results are purely combinatorial and do not involve logic. We show that trails avoiding forbidden transitions,…
Given a pair of graphs with the same number of vertices, the inexact graph matching problem consists in finding a correspondence between the vertices of these graphs that minimizes the total number of induced edge disagreements. We study…
In the matching interdiction problem, we are given an undirected graph with weights and interdiction costs on the edges and seek to remove a subset of the edges constrained to some budget, such that the weight of a maximum weight matching…
Interdiction problems are leader-follower games in which the leader is allowed to delete a certain number of edges from the graph in order to maximally impede the follower, who is trying to solve an optimization problem on the impeded…
A matching $M$ in a graph $G$ is said to be uniquely restricted if there is no other matching in $G$ that matches the same set of vertices as $M$. We describe a polynomial-time algorithm to compute a maximum cardinality uniquely restricted…
We introduce a novel model-theoretic framework inspired from graph modification and based on the interplay between model theory and algorithmic graph minors. The core of our framework is a new compound logic operating with two types of…
Tolerance graphs model interval relations in such a way that intervals can tolerate a certain degree of overlap without being in conflict. This subclass of perfect graphs has been extensively studied, due to both its interesting structure…
In this paper, we provide polynomial-time algorithms for different extensions of the matching counting problem, namely maximal matchings, path matchings (linear forest) and paths, on graph classes of bounded clique-width. For maximal…
Best match graphs (BMG) are a key intermediate in graph-based orthology detection and contain a large amount of information on the gene tree. We provide a near-cubic algorithm to determine whether a BMG is binary-explainable, i.e., whether…
Graphs are mathematical tools that can be used to represent complex real-world interconnected systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently.…
We show that the perfect matching problem in general graphs is in Quasi-NC. That is, we give a deterministic parallel algorithm which runs in $O(\log^3 n)$ time on $n^{O(\log^2 n)}$ processors. The result is obtained by a derandomization of…
Considering the worst-case scenario, junction tree algorithm remains the most general solution for exact MAP inference with polynomial run-time guarantees. Unfortunately, its main tractability assumption requires the treewidth of a…
This paper presents proof nets for multiplicative-additive linear logic (MALL), called conflict nets. They are efficient, since both correctness and translation from a proof are p-time (polynomial time), and abstract, since they are…
Fast exact algorithms are known for Hamiltonian paths in undirected and directed bipartite graphs through elegant though involved algorithms that are quite different from each other. We devise algorithms that are simple and similar to each…
In a 1977 paper, Steffens identified an elegant criterion for determining when a countable graph has a perfect matching. In this paper, we will investigate the proof-theoretic strength of this result and related theorems. We show that a…
We study the graphs formed from instances of the stable matching problem by connecting pairs of elements with an edge when there exists a stable matching in which they are matched. Our results include the NP-completeness of recognizing…
We study the perfect matching lattice of a matching covered graph $G$, generated by the incidence vectors of its perfect matchings. Building on results of Lov\'asz and de Carvalho, Lucchesi, and Murty, we give a polynomial-time algorithm…
Coding theory is very useful for real world applications. A notable example is digital television. Basically, coding theory is to study a way of detecting and/or correcting data that may be true or false. Moreover coding theory is an area…
In the Exact Matching Problem (EM), we are given a graph equipped with a fixed coloring of its edges with two colors (red and blue), as well as a positive integer $k$. The task is then to decide whether the given graph contains a perfect…
We establish a connection between problems studied in rigidity theory and matroids arising from linear algebraic constructions like tensor products and symmetric products. A special case of this correspondence identifies the problem of…