离散数学
This paper considers synchronous discrete-time dynamical systems on graphs based on the threshold model. It is well known that after a finite number of rounds these systems either reach a fixed point or enter a 2-cycle. The problem of…
A total coloring of a graph $G = (V, E)$ is an assignment of colors to vertices and edges such that neither two adjacent vertices nor two incident edges get the same color, and, for each edge, the end-points and the edge itself receive…
Epiphainein counts unreachable single-side pawn diagrams (in chess) where pawns can move forward or diagonally-forward without limit whilst remaining on the board. Epiphainein is a serial calculation and takes a few seconds to calculate the…
Recent research has examined algorithms to minimize robots' resource footprints. The class of combinatorial filters (discrete variants of widely-used probabilistic estimators) has been studied and methods for reducing their space…
We consider the allocation of $m$ balls into $n$ bins with incomplete information. In the classical Two-Choice process a ball first queries the load of two randomly chosen bins and is then placed in the least loaded bin. In our setting,…
In this paper we look at the problem of adjacency labeling of graphs. Given a family of undirected graphs the problem is to determine an encoding-decoding scheme for each member of the family such that we can decode the adjacency…
Grid intersection graphs are the intersection graphs of vertical and horizontal segments in the plane. When the bottom and respectively left endpoints of the vertical and horizontals segments belong to a line with negative slope, the graph…
This paper studies three classes of cellular automata from a computational point of view: freezing cellular automata where the state of a cell can only decrease according to some order on states, cellular automata where each cell only makes…
Twin-width is a newly introduced graph width parameter that aims at generalizing a wide range of "nicely structured" graph classes. In this work, we focus on obtaining good bounds on twin-width $\text{tww}(G)$ for graphs $G$ from a number…
We introduce the notion of de Bruijn entropy of an Eulerian quiver and show how the corresponding relative entropy can be applied to practical string similarity problems. This approach explicitly links the combinatorial and…
We give a modern account of Agafonov's original proof of his eponymous theorem. The original proof was only reported in Russian in a journal not widely available, and the work most commonly cited in western literature is instead the English…
We consider hard-disc mixtures with disc sizes within ratio $\sqrt{2}-1$, that is, the small disc exactly fits in the hole between four large discs. For each prescribed stoichiometry of large and small discs, the densest packings are…
Let $f$ be a polynomial of degree $d$ in $n$ variables over a finite field $\mathbb{F}$. The polynomial is said to be unbiased if the distribution of $f(x)$ for a uniform input $x \in \mathbb{F}^n$ is close to the uniform distribution over…
We show that there exists no algorithm that decides for any bilinear system $(B,v)$ if the growth rate of $(B,v)$ is $1$. This answers a question of Bui who showed that if the coefficients are positive the growth rate is computable (i.e.,…
For two given nonnegative integers $h$ and $k$, an $L(h,k)$-edge labeling of a graph $G$ is the assignment of labels $\{0,1, \cdots, n\}$ to the edges so that two edges having a common vertex are labeled with difference at least $h$ and two…
Eternal vertex cover problem is a variant of the classical vertex cover problem modeled as a two player attacker-defender game. Computing eternal vertex cover number of graphs is known to be NP-hard in general and the complexity status of…
The Monte Carlo simulation (MCS) is a statistical methodology used in a large number of applications. It uses repeated random sampling to solve problems with a probability interpretation to obtain high-quality numerical results. The MCS is…
We propose a new deterministic methodology to predict RNA sequence and protein folding. Is stem enough for structure prediction? The main idea is to consider all possible stem formation in the given sequence. With the stem loop energy and…
Recently, random walks on dynamic graphs have been studied because of their adaptivity to the time-varying structure of real-world networks. In general, there is a tremendous gap between static and dynamic graph settings for the lazy simple…
A word $w$ of letters on edges of underlying graph $\Gamma$ of deterministic finite automaton (DFA) is called synchronizing if $w$ sends all states of the automaton to a unique state. J. \v{C}erny discovered in 1964 a sequence of $n$-state…