Heterogeneous information networks (HINs) are widely employed for describing real-world data with intricate entities and relationships. To automatically utilize their semantic information, graph neural architecture search has recently been developed various tasks of HINs. Existing works, on the other hand, show weaknesses in instability inflexibility. address these issues, we propose a novel me...

A multigraph is degree-splittable if it decomposes into two submultigraphs whose degree lists are the same, plus one leftover edge when the total number of edges is odd. We prove that a connected multigraph is degree-splittable if it has an even number of vertices of each odd degree. For caterpillars, we characterize the splittable caterpillars with diameter at most 4, provide a general suffici...

We give graphical characterisation of the access structure to both classical and quantum information encoded onto a multigraph defined for prime dimension q, as well as explicit decoding operations for quantum secret sharing based on graph state protocols. We give a lower bound on k for the existence of a ((k, n))q scheme and prove, using probabilistic methods, that there exists α such that a r...

Given a family F of multigraphs without isolated vertices, a multigraph M is called F-decomposable if M is an edge disjoint union of multigraphs each of which is isomorphic to a member of F . We present necessary and sufficient conditions for the existence of such decompositions if F comprises two multigraphs from the set consisting of a 2-cycle, a 2-matching and a path with two edges.

Let G be a multipartite multigraph without loops. Then G is said to be internally fair if its edges are shared as evenly as possible among all pairs of its partite sets. An internally fair factorization of G is an edge-decomposition of G into internally fair regular spanning subgraphs. A holey factor of G is a regular subgraph spanning all vertices but one partite set. An internally fair holey ...

In this paper, we consider a number of results and six conjectures on properly coloured (PC) paths and cycles in edge-coloured multigraphs. We overview some known results and prove new ones. In particular, we consider a family of transformations of an edge-coloured multigraph G into an ordinary graph that allow us to check the existence of PC cycles and PC (s, t)-paths in G and, if they exist, ...

Consider a random multigraph G∗ with given vertex degrees d1, . . . , dn, constructed by the configuration model. We give a new proof of the fact that, asymptotically for a sequence of such multigraphs with the number of edges 1 2 ∑ i di → ∞, the probability that the multigraph is simple stays away from 0 if and only if ∑ i d 2 i = O (∑ i di ) . The new proof uses the method of moments, which m...

Let k be a positive integer, Sk and Ck denote, respectively, a star and a cycle of k edges. λKn is the usual notation for the complete multigraph on n vertices and in which every edge is taken λ times. In this paper, we investigate necessary and sufficient conditions for the existence of the decomposition of λKn into edges disjoint of stars Sk’s and cycles Ck’s.

Many real world datasets can be represented by graphs with a set of nodes interconnected with each other by multiple relations (e.g., social network, RDF graph, biological data). Such a rich graph, called multigraph, is well suited to represent real world scenarios with complex interactions. However, performing subgraph query on multigraphs is still an open issue since, unfortunately, all the e...