Related papers: Closed graphs and open maps
We generalize the van Kampen theorem for unions of non-connected spaces, due to R. Brown and A. R. Salleh, to the context where families of subspaces of a space B are replaced by a locally sectionable map to B.
Many NLP applications can be framed as a graph-to-sequence learning problem. Previous work proposing neural architectures on this setting obtained promising results compared to grammar-based approaches but still rely on linearisation…
We prove that Menger's theorem is valid for infinite graphs, in the following strong form: let $A$ and $B$ be two sets of vertices in a possibly infinite digraph. Then there exist a set $\cp$ of disjoint $A$-$B$ paths, and a set $S$ of…
Signed graphs have their edges labeled either as positive or negative. Here we introduce two types of signed distance matrix for signed graphs. We characterize balance in signed graphs using these matrices and we obtain explicit formulae…
The processes of constructing some graphs from others using binary operations of union with intersection (gluing) are studied. For graph classes closed with respect to gluing operations the elemental and operational bases are introduced.…
A new kind of diagrams is presented, showing the causal structure of bimetric interactions.
We apply a recent duality theorem for tangles in abstract separation systems to derive tangle-type duality theorems for width-parameters in graphs and matroids. We further derive a duality theorem for the existence of clusters in large data…
We give a new proof of K\"onig's theorem and generalize the Gallai-Edmonds decomposition to balanced hypergraphs in two different ways. Based on our decompositions we give two new characterizations of balanced hypergraphs and show some…
We give a brief survey of recent results on word maps on simple groups and polynomial maps on simple associative and Lie algebras. Our focus is on parallelism between these theories, allowing one to state many new open problems and giving…
We study topological properties of the graph topology.
We consider infinite connected quasi-transitive locally finite graphs and show that every such graph with more than one end is a tree amalgamation of two other such graphs. This can be seen as a graph-theoretical version of Stallings'…
We prove that any closed map between metrizable spaces can be extended to a closed map between completely metrizable spaces with the same extensional dimension.
We consider two notions describing how one finite graph may be larger than another. Using them, we prove several theorems for such pairs that compare the number of spanning trees, the return probabilities of random walks, and the number of…
The presented material is devoted to the equivalent conversion from the vertex graphs to the edge graphs. We suggest that the proved theorems solve the problem of the isomorphism of graphs, the problem of the graph's enumeration with the…
In this paper we study the geometry of graph spaces endowed with a special class of graph edit distances. The focus is on geometrical results useful for statistical pattern recognition. The main result is the Graph Representation Theorem.…
Perfect code in Cayley graphs and Cayley sum graphs is studied extensively in recent years. In this paper, we consider perfect code in generalized Cayley graphs.
We prove a general duality theorem for tangle-like dense objects in combinatorial structures such as graphs and matroids. This paper continues, and assumes familiarity with, the theory developed in [6]
Immersions of graphs to the projective plane are studied. A classification of immersions up to regular homotopy is given. A complete invariant of immersions up to regular homotopy is constructed. Equivalence classes are described.
In this paper, a survey about recent progress on problems solved using graph amalgamations is presented, along with some new results with complete proofs, and some related open problems.
A self-contained exposition is given of the topological and Galois-theoretic properties of the category of combinatorial 1-complexes, or graphs, very much in the spirit of Stallings. A number of classical, as well as some new results about…