Related papers: Good sequencings for small directed triple systems
The girth of a graph $G$ is the length of a shortest cycle of $G$. Jiang (JCT-B, 2001) showed that every graph $G$ with girth at least $2\ell+1$ and minimum degree at least $k/\ell$ contains every tree $T$ with $k$ edges whose maximum…
The transmission of a vertex $v$ of a graph $G$ is the sum of distances from $v$ to all the other vertices in $G$. A graph is transmission irregular if all of its vertices have pairwise different transmissions. A starlike tree…
Sequential computation increasingly produces long traces containing nested branches, status transitions, textual payloads, and compact summaries of earlier execution. This paper introduces budgeted dynamic trace structures (BDTS), a…
Given a graph $G$, a subset $S$ of vertices of $G$ is an efficient dominating set ($EDS$) if $|N[v] \cap S|=1,$ for all $v\in V(G)$. A graph $G$ is efficiently dominatable if it possesses an $EDS$. The efficient domination number of G is…
A set $S$ of vertices of a digraph $D$ is called an open neighbourhood locating-dominating set if every vertex in $D$ has an in-neighbour in $S$, and for every pair $u,v$ of vertices of $D$, there is a vertex in $S$ that is an in-neighbour…
A $k$-dominating set is a set $D$ of nodes of a graph such that, for each node $v$, there exists a node $w \in D$ at distance at most $k$ from $v$. Our aim is the deterministic distributed construction of small $T$-dominating sets in time…
We prove that for every set $S$ of vertices of a directed graph $D$, the maximum number of vertices in $S$ contained in a collection of vertex-disjoint cycles in $D$ is at least the minimum size of a set of vertices that hits all cycles…
Fractional repetition (FR) codes is a family of codes for distributed storage systems (DSS) that allow uncoded exact repairs with minimum repair bandwidth. In this work, we consider a bound on the maximum amount of data that can be stored…
The $\Delta$-edge stability number ${\rm es}_{\Delta}(G)$ of a graph $G$ is the minimum number of edges of $G$ whose removal results in a subgraph $H$ with $\Delta(H) = \Delta(G)-1$. Sets whose removal results in a subgraph with smaller…
Consider a generalized multiterminal source coding system, where $\ell\choose m$ encoders, each observing a distinct size-$m$ subset of $\ell$ ($\ell\geq 2$) zero-mean unit-variance symmetrically correlated Gaussian sources with correlation…
A sequence of positive integers $(a_1,a_2,\ldots,a_k)$ is called $\ell$-additive if $a_1+a_2+\cdots+a_k=\ell a_1$ or $\ell a_k$. In this paper, we prove that for all $k\geq3$, if $n$ is sufficiently large, then every permutation of…
Rewrite systems [6, 10, 12] have been widely employing equality saturation [9], which is an optimisation methodology that uses a saturated e-graph to represent all possible sequences of rewrite simultaneously, and then extracts the optimal…
In a graph $G$, a subset of vertices is a dissociation set if it induces a subgraph with vertex degree at most 1. A maximum dissociation set is a dissociation set of maximum cardinality. The dissociation number of $G$, denoted by $\psi(G)$,…
A $k$-tuple total dominating set ($k$TDS) of a graph $G$ is a set $S$ of vertices in which every vertex in $G$ is adjacent to at least $k$ vertices in $S$. The minimum size of a $k$TDS is called the $k$-tuple total dominating number and it…
The design of multitarget rendezvous missions requires a method to quickly and accurately approximate the optimal transfer between any two rendezvous targets. In this paper, a deep neural network (DNN)-based method is proposed for quickly…
A graceful difference labeling (gdl for short) of a directed graph G with vertex set V is a bijection f between V and {1,...,|V|} such that, when each arc uv is assigned the difference label f(v)-f(u), the resulting arc labels are distinct.…
Let $1 \le s < t$, $N \ge 1$ be integers and a complex electronic circuit of size $t$ is said to be an $s$-active, $\; s \ll t$, and can work as a system block if not more than $s$ elements of the circuit are defective. Otherwise, the…
Sets of sequences with good correlation properties are desired in many active sensing and communication systems, e.g., multiple-input-multiple-output (MIMO) radar systems and code-division multiple-access (CDMA) cellular systems. In this…
In the Directed Feedback Vertex Set (DFVS) problem, the input is a directed graph $D$ on $n$ vertices and $m$ edges, and an integer $k$. The objective is to determine whether there exists a set of at most $k$ vertices intersecting every…
Motivated by the duplication-correcting problem for data storage in live DNA, we study the construction of constant-weight codes in $\ell_1$-metric. By using packings and group divisible designs in combinatorial design theory, we give…