Related papers: Uniformly resolvable decompositions of K_v into pa…

In this paper we consider the uniformly resolvable decompositions of the complete graph $K_v$, or the complete graph minus a 1-factor as appropriate, into subgraphs such that each resolution class contains only blocks isomorphic to the same…

In this paper we consider the complex uniformly resolvable decompositions of the complete graph $K_v$ into subgraphs such that each resolution class contains only blocks isomorphic to the same graph from a given set $\mathcal H$. We…

In this paper we consider the uniformly resolvable decompositions of the complete graph $2K_v$ into subgraphs where each resolution class contains only blocks isomorphic to the same graph. We completely determine the spectrum for the cases…

We consider the existence problem of uniformly resolvable decompositions of $K_v$ into subgraphs such that each resolution class contains only blocks isomorphic to the same graph. We give a complete solution for the case in which one…

We consider uniformly resolvable decompositions of $K_v$ into subgraphs such that each resolution class contains only blocks isomorphic to the same graph. We give a complete solution for the case in which one resolution class is $K_2$ and…

We consider uniformly resolvable decompositions of $K_v$ into subgraphs such that each resolution class contains only blocks isomorphic to the same graph. We give a partial solution for the case in which all resolution classes are either…

In this article we completely determine the spectrum for uniformly resolvable decompositions of the complete graph K_v into r 1-factors and s classes containing only copies of h-suns.

Let $K_v$ denote the complete graph of order $v$ and $K_v - I$ denote $K_v$ minus a 1-factor. In this article we investigate uniformly resolvable decompositions of $K_v$ and $K_v-I$ into $r$ classes containing only copies of $3$-stars and…

In this paper it is established that a decomposition of a 3-uniform hypergraph K_v^{(3)} into a special kind of hypergraph K_4^{(3)}+e exists if and only if v\equiv 0,1,2 (mod 5) and v\geq 7.

The complete symmetric directed graph of order $v$, denoted $K_{v}^*$, is the directed graph on $v$ vertices that contains both arcs $(x,y)$ and $(y,x)$ for each pair of distinct vertices $x$ and $y$. For a given directed graph, $D$, the…

We study the isomorphism problem for random hypergraphs. We show that it is solvable in polynomial time for the binomial random $k$-uniform hypergraph $H_{n,p;k}$, for a wide range of $p$. We also show that it is solvable w.h.p. for random…

Motivated by the wide-ranging applications of Hamiltonian decompositions in distributed computing, coded caching, routing, resource allocation, load balancing, and fault tolerance, our work presents a comprehensive design for Hamiltonian…

For a given $\pi=(\pi_0, \pi_1,..., \pi_k) \in \{0, 1, *\}^{k+1}$, we want to determine whether an input $k$-uniform hypergraph $G=(V, E)$ has a partition $(V_1, V_2)$ of the vertex set so that for all $X \subseteq V$ of size $k$, $X \in E$…

We consider edge decompositions of $K_v^{(3)}-I$, the complete 3-uniform hypergraph of order $v$ minus a 1-factor (parallel class, packing of $v/3$ disjoint edges). We prove that a decomposition into tight 6-cycles exists if and only if…

Following standard terminology, $\lambda K_v$ is a multigraph on $v$ vertices such that $\lambda$ edges join each pair of vertices. Let $(\lambda+\mu)K_{v+u}-\lambda K_v$ be the graph $(V\cup U,E)$ with $|V|=v$, $|U|=u$, and…

Unigraphs are graphs uniquely determined by their own degree sequence up to isomorphism. There are many subclasses of unigraphs such as threshold graphs, split matrogenic graphs, matroidal graphs, and matrogenic graphs. Unigraphs and these…

Let $(X,E_X)$ and $(V,E_V)$ be finite connected graphs without loops. We assume that $V$ has two distinguished vertices $a,b$ and an automorphism $\gamma$ which exchanges $a$ and~$b$. The $V$-edge substitution of $X$ is the graph $X[V]$…

This article explores a new way to obtain the optimal decomposition of a complete graph of order 18 and 19 into cliques of order 3 and 4.

For any field $K$ and for a completely arbitrary graph $E$, we characterize the Leavitt path algebras $L_K(E)$ that are indecomposable (as a direct sum of two-sided ideals) in terms of the underlying graph. When the algebra decomposes, it…

We identify a set of quantum graphs with unique and precisely defined spectral properties called {\it regular quantum graphs}. Although chaotic in their classical limit with positive topological entropy, regular quantum graphs are…