离散数学
Directed cographs (di-cographs) play a crucial role in the reconstruction of evolutionary histories of genes based on homology relations which are binary relations between genes. A variety of methods based on pairwise sequence comparisons…
An unceasing problem of our prevailing society is the fair division of goods. The problem of proportional cake cutting focuses on dividing a heterogeneous and divisible resource, the cake, among $n$ players who value pieces according to…
In a recent breakthrough STOC~2015 paper, a continuous diffusion process was considered on hypergraphs (which has been refined in a recent JACM 2018 paper) to define a Laplacian operator, whose spectral properties satisfy the celebrated…
An edge labeling of a graph distinguishes neighbors by sets (multisets, resp.), if for any two adjacent vertices $u$ and $v$ the sets (multisets, resp.) of labels appearing on edges incident to $u$ and $v$ are different. In an analogous way…
Minimizing the sum of weighted completion times on $m$ identical parallel machines is one of the most important and classical scheduling problems. For the stochastic variant where processing times of jobs are random variables, M\"ohring,…
The Student-Project Allocation problem with preferences over Projects (SPA-P) involves sets of students, projects and lecturers, where the students and lecturers each have preferences over the projects. In this context, we typically seek a…
There are various topological indices for example distance based topological indices and degree based topological indices etc. In QSAR/QSPR study, physiochemical properties and topological indices for example atom bond connectivity index,…
We introduce a new framework for reconfiguration problems, and apply it to independent sets as the first example. Suppose that we are given an independent set $I_0$ of a graph $G$, and an integer $l \ge 0$ which represents a lower bound on…
Fitch graphs $G=(X,E)$ are di-graphs that are explained by $\{\otimes,1\}$-edge-labeled rooted trees with leaf set $X$: there is an arc $xy\in E$ if and only if the unique path in $T$ that connects the least common ancestor…
A perfect matching in an undirected graph $G=(V,E)$ is a set of vertex disjoint edges from $E$ that include all vertices in $V$. The perfect matching problem is to decide if $G$ has such a matching. Recently Rothvo{\ss} proved the striking…
A polyhedron is box-integer if its intersection with any integer box $\{\ell\leq x \leq u\}$ is integer. We define principally box-integer polyhedra to be the polyhedra $P$ such that $kP$ is box-integer whenever $kP$ is integer. We…
We are given an integer $d$, a graph $G=(V,E)$, and a uniformly random embedding $f : V \rightarrow \{0,1\}^d$ of the vertices. We are interested in the probability that $G$ can be "realized" by a scaled Euclidean norm on $\mathbb{R}^d$, in…
We study the structure learning problem for $H$-colorings, an important class of Markov random fields that capture key combinatorial structures on graphs, including proper colorings and independent sets, as well as spin systems from…
Let $G=(V,A)$ be a directed graph without parallel arcs, and let $S\subseteq V$ be a set of vertices. Let the sequence $S=S_0\subseteq S_1\subseteq S_2\subseteq\cdots$ be defined as follows: $S_1$ is obtained from $S_0$ by adding all…
The present paper contains additional asymptotic result over an earlier investigation of Kapelko and Kranakis. Consider $n$ mobile sensors placed independently at random with the uniform distribution on the unit interval $[0,1]$. Fix $a$ an…
Many applications in graph theory are motivated by routing or flow problems. Among these problems is Steiner Orientation: given a mixed graph G (having directed and undirected edges) and a set T of k terminal pairs in G, is there an…
The 2048 game involves tiles labeled with powers of two that can be merged to form bigger powers of two; variants of the same puzzle involve similar merges of other tile values. We analyze the maximum score achievable in these games by…
We introduce the notion of \emph{stab number} and \emph{exact stab number} of rectangle intersection graphs, otherwise known as graphs of boxicity at most 2. A graph $G$ is said to be a \emph{$k$-stabbable rectangle intersection graph}, or…
Consider the stable matching problem on two sets. We introduce the concept of a preference cycle and show how its natural presence in stable matchings proves a series of classical results in an elementary way.
We consider generalizations of parity polytopes whose variables, in addition to a parity constraint, satisfy certain ordering constraints. More precisely, the variable domain is partitioned into $k$ contiguous groups, and within each group,…