离散数学
The reload cost refers to the cost that occurs along a path on an edge-colored graph when it traverses an internal vertex between two edges of different colors. Galbiati et al.[1] introduced the Minimum Reload Cost Cycle Cover problem,…
A graph is called equimatchable if all of its maximal matchings have the same size. Frendrup et al. [8] provided a characterization of equimatchable graphs with girth at least $5$. In this paper, we extend this result by providing a…
A long-standing conjecture by Heath, Pemmaraju, and Trenk states that the upward book thickness of outerplanar DAGs is bounded above by a constant. In this paper, we show that the conjecture holds for subfamilies of upward outerplanar…
Full binary trees naturally represent commutative non-associative products. There are many important examples of these products: finite-precision floating-point addition and NAND gates, among others. Balance in such a tree is highly…
Many cluster similarity indices are used to evaluate clustering algorithms, and choosing the best one for a particular task remains an open problem. We demonstrate that this problem is crucial: there are many disagreements among the…
Discrete orthogonal matrices have several applications in information technology, such as in coding and cryptography. It is often challenging to generate discrete orthogonal matrices. A common approach widely in use is to discretize…
In this paper, we present two new concepts related to subgraph counting where the focus is not on the number of subgraphs that are isomorphic to some fixed graph $H$, but on the frequency with which a vertex or an edge belongs to such…
We present a strengthened version of a lemma due to Bondy and Lov\'asz. This lemma establishes the connectivity of a certain graph whose nodes correspond to the spanning trees of a 2-vertex-connected graph, and implies the k=2 case of the…
Quantum annealing is an emerging new platform for combinatorial optimization, requiring an Ising model formulation for optimization problems. The formulation can be an essential obstacle to the permeation of this innovation into broad areas…
Finding the exact integrality gap $\alpha$ for the LP relaxation of the 2-edge-connected spanning multigraph problem (2EC) is closely related to the same problem for the Held-Karp relaxation of the metric traveling salesman problem (TSP).…
Graphs are a central object of study in various scientific fields, such as discrete mathematics, theoretical computer science and network science. These graphs are typically studied using combinatorial, algebraic or probabilistic methods,…
Proposed initially from a practical circumstance, the traveling salesman problem caught the attention of numerous economists, computer scientists, and mathematicians. These theorists were instead intrigued by seeking a systemic way to find…
We prove the equidistribution of several multistatistics over some classes of permutations avoiding a $3$-length pattern. We deduce the equidistribution, on the one hand of inv and foze" statistics, and on the other hand that of maj and…
Let $L = \{\frac{a_1}{b_1}, \ldots , \frac{a_s}{b_s}\}$, where for every $i \in [s]$, $\frac{a_i}{b_i} \in [0,1)$ is an irreducible fraction. Let $\mathcal{F} = \{A_1, \ldots , A_m\}$ be a family of subsets of $[n]$. We say $\mathcal{F}$ is…
We develop an algorithm for computing the weight distribution of a linear $[n,k]$ code over a finite field $\mathbb{F}_q$. We represent the codes by their characteristic vector with respect to a given generator matrix and a special type of…
The effect of adjusting damping factor {\alpha}, from a small initial value {\alpha}0 to the final desired {\alpha}f value, upon then iterations needed for PageRank computation is observed. Adjustment of the damping factor is done in one or…
We study the dynamic and complexity of the generalized Q2R automaton. We show the existence of non-polynomial cycles as well as its capability to simulate with the synchronous update the classical version of the automaton updated under a…
Inferring the potential consequences of an unobserved event is a fundamental scientific question. To this end, Pearl's celebrated do-calculus provides a set of inference rules to derive an interventional probability from an observational…
Pearl's d-separation is a foundational notion to study conditional independence between random variables. We define the topological conditional separation and we show that it is equivalent to the d-separation, extended beyond acyclic…
The effect of adjusting damping factor {\alpha} and tolerance {\tau} on iterations needed for PageRank computation is studied here. Relative performance of PageRank computation with L1, L2, and L{\infty} norms used as convergence check, are…