Related papers: Graphs with Non-unique Decomposition and Their Ass…
Graph is an abstract representation commonly used to model networked systems and structure. In problems across various fields, including computer vision and pattern recognition, and neuroscience, graphs are often brought into comparison (a…
In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques…
Typically, graph structures are represented by one of three different matrices: the adjacency matrix, the unnormalised and the normalised graph Laplacian matrices. The spectral (eigenvalue) properties of these different matrices are…
A triangle decomposition of a graph is a partition of its edges into triangles. A fractional triangle decomposition of a graph is an assignment of a non-negative weight to each of its triangles such that the sum of the weights of the…
A degree-regular triangulation is one in which each vertex has identical degree. Our main result is that any such triangulation of a (possibly non-compact) surface $S$ is geometric, that is, it is combinatorially equivalent to a geodesic…
A Hamiltonian decomposition of a regular graph is a partition of its edge set into Hamiltonian cycles. The problem of finding edge-disjoint Hamiltonian cycles in a given regular graph has many applications in combinatorial optimization and…
It is shown that for a constant $t\in \mathbb{N}$, every simple topological graph on $n$ vertices has $O(n)$ edges if it has no two sets of $t$ edges such that every edge in one set is disjoint from all edges of the other set (i.e., the…
We introduce a characterization for split graphs by using edge contraction. Then, we use it to prove that any ($2K_{2}$, claw)-free graph with $\alpha(G) \geq 3$ is a split graph. Also, we apply it to characterize any pseudo-split graph.…
A map is a connected topological graph $\Gamma$ cellularly embedded in a surface. In this paper, applying Tutte's algebraic representation of map, new ideas for enumerating non-equivalent orientable or non-orientable maps of graph are…
Girth-regular graphs with equal girth, regular degree and chromatic index are studied for the determination of 1-factorizations with each 1-factor intersecting every girth cycle. Applications to hamiltonian decomposability and to…
Every finite graph $G$ can be decomposed in a canonical way that displays its local connectivity-structure [DJKK26]. These decompositions are defined via a suitable more tree-like covering of $G$, whose tangle-tree structure is projected…
We extend the theory of equitable decompositions, in which, if a graph has a particular type of symmetry, i.e. a uniform or basic automorphism $\phi$, it is possible to use $\phi$ to decompose a matrix $M$ appropriately associated with the…
Inspired by notorious combinatorial optimization problems on graphs, in this paper we consider a series of related problems defined using a metric space and topology determined by a graph. Particularly, we present the Independent Set,…
In this paper we establish links between, and new results for, three problems that are not usually considered together. The first is a matrix decomposition problem that arises in areas such as statistical modeling and signal processing:…
This article provides structural characterization of simple graphs whose edge-set can be partitioned into maximum matchings. We use Vizing's classification of simple graphs based on edge chromatic index.
To enumerate 3-manifold triangulations with a given property, one typically begins with a set of potential face pairing graphs (also known as dual 1-skeletons), and then attempts to flesh each graph out into full triangulations using an…
For a given hypergraph, an orientation can be assigned to the vertex-edge incidences. This orientation is used to define the adjacency and Laplacian matrices. In addition to studying these matrices, several related structures are…
We observe that certain large-clique graph triangulations can be useful to reduce both computational and space requirements when making queries on mixed stochastic/deterministic graphical models. We demonstrate that many of these…
We describe two constructions of (very) dense graphs which are edge disjoint unions of large {\em induced} matchings. The first construction exhibits graphs on $N$ vertices with ${N \choose 2}-o(N^2)$ edges, which can be decomposed into…
We establish new bounds on the minimum number of distinct eigenvalues among real symmetric matrices with nonzero off-diagonal pattern described by the edges of a graph and apply these to determine the minimum number of distinct eigenvalues…