相关论文: Twofold triple systems with cyclic 2-intersecting …

We investigate the structure of graphs of twin-width at most $1$, and obtain the following results: - Graphs of twin-width at most $1$ are permutation graphs. In particular they have an intersection model and a linear structure. - There is…

We investigate coding schemes that map source symbols into multisets of an alphabet set. Such a formulation of source coding is an alternative approach to the traditional framework and is inspired by an object tracking problem over…

In this paper, we consider some general properties of block graphs as well as the equitable coloring problem in this class of graphs. In the first part we establish the relation between two structural parameters for general block graphs. We…

Let $G$ be a group and $S$ be the set of all non-trivial proper subgroups of $G$. The intersection hypergraph of $G$, denoted by $\tilde{\Gamma}_\mathcal{H}(G)$, is a hypergraph whose vertex set is $\{H \in S \,\, | \,\, H \cap K = \{e\}…

We study the multicolour discrepancy of spanning trees and Hamilton cycles in graphs. As our main result, we show that under very mild conditions, the $r$-colour spanning-tree discrepancy of a graph $G$ is equal, up to a constant, to the…

We present results on partitioning the vertices of $2$-edge-colored graphs into monochromatic paths and cycles. We prove asymptotically the two-color case of a conjecture of S\'ark\"ozy: the vertex set of every $2$-edge-colored graph can be…

Random $s$-intersection graphs have recently received considerable attention in a wide range of application areas. In such a graph, each vertex is equipped with a set of items in some random manner, and any two vertices establish an…

We study the Balanced Connected Subgraph(shortly, BCS) problem on geometric intersection graphs such as interval, circular-arc, permutation, unit-disk, outer-string graphs, etc. Given a vertex-colored graph $G=(V,E)$, where each vertex in…

This paper studies graphs that have two tree decompositions with the property that every bag from the first decomposition has a bounded-size intersection with every bag from the second decomposition. We show that every graph in each of the…

In this work, we classify the circuit binomials of any weighted oriented graph $D$ and we explicitly compute the circuit binomials of $D$ in terms of the minors of the incidence matrix of $D$. We show that the circuit binomials of any…

A combinatorial Gray code for a class of objects is a listing that contains each object from the class exactly once such that any two consecutive objects in the list differ only by a `small change'. Such listings are known for many…

Recently, van der Hofstad, Komj\'{a}thy, and Vadon (2022) identified the critical point for the emergence of a giant connected component for the bipartite configuration model (BCM) and used this to analyze its associated random intersection…

We study $M$-alternating Hamilton paths and $M$-alternating Hamilton cycles in a simple connected graph $G$ on $\nu$ vertices with a perfect matching $M$. Let $G$ be a bipartite graph, we prove that if for any two vertices $x$ and $y$ in…

The $k$-token graph $T_k(G)$ is the graph whose vertices are the $k$-subsets of vertices of a graph $G$, with two vertices of $T_k(G)$ adjacent if their symmetric difference is an edge of $G$. We explore when $T_k(G)$ is a well-covered…

We study upper bounds on the size of optimum locating-total dominating sets in graphs. A set $S$ of vertices of a graph $G$ is a locating-total dominating set if every vertex of $G$ has a neighbor in $S$, and if any two vertices outside $S$…

A graph G is dually chordal if there is a spanning tree T of G such that any maximal clique of G induces a subtree in T. This paper investigates the Colourability problem on dually chordal graphs. It will show that it is NP-complete in case…

The intersection graph of a collection of trapezoids with corner points lying on two parallel lines is called a trapezoid graph. These graphs and their generalizations were applied in various fields, including modeling channel routing…

Let $G=(V,E)$ be a finite, simple graph. We consider for each oriented graph $G_{\cal O}$ associated to an orientation ${\cal O}$ of the edges of $G$, the toric ideal $P_{G_{\cal O}}$. In this paper we study those graphs with the property…

The problem of finding a maximum $2$-matching without short cycles has received significant attention due to its relevance to the Hamilton cycle problem. This problem is generalized to finding a maximum $t$-matching which excludes specified…

A remarkable result at the intersection of number theory and group theory states that the order of a finite group $G$ (denoted $|G|$) is divisible by the dimension $d_R$ of any irreducible complex representation of $G$. We show that the…