The face pairing graph of a 3-manifold triangulation is a 4-valent graph denoting which tetrahedron faces are identified with which others. We present a series of properties that must be satisfied by the face pairing graph of a closed minimal P-irreducible triangulation. In addition we present constraints upon the combinatorial structure of such a triangulation that can be deduced from its face...

Counting the number of imbeddings in various surfaces of each of the graphs in an interesting family is an ongoing topic in topological graph theory. Our special focus here is on a family of closed chains of copies of a given graph. We derive double-root partials for open chains of copies of a given graph, and we then apply a self-amalgamation theorem, thereby obtaining genus distributions for ...

For p∈N, a coloring λ of the vertices graph G is p-centered if for every connected subgraph H G, either receives more than p colors under or there color that appears exactly once in H. Centered colorings play an important role theory sparse classes introduced by Nešetřil and Ossona de Mendez [31], [32], as they structurally characterize bounded expansion — one key sparsity notions this theory. ...

Several notions on soft topology are studied and their basic properties investigated by using the concept of pre open sets closure operator which derived from basics set theory established Molodtsov [1]. In this paper we introduce some separation axioms called Soft R0 R1 in topological spaces defined over an initial universe with a fixed parameters. Many characterizations these have been demons...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 26 November 2018Accepted: 06 2020Published online: 21 January 2021Keywordsimmersions, tree-cut width, graph modification problems, edge-deletion distance, kernelizationAMS Subject Headings05C70, 05C75, 05C83, 05C85Publication DataISSN (print): 0895-4801ISSN (online): 1095...

Let G be a minor-closed graph class. We say that is k-apex of if contains set S at most k vertices such G?S belongs to G. denote by Ak(G) the all graphs are k-apices prove every in obstruction Ak(G), i.e., minor-minimal not belonging has order 2222poly(k), where poly polynomial function whose degree depends on minor-obstructions This bound drops 22poly(k) when excludes some apex as minor.

A monumental project in graph theory was recently completed. The project, started by Robertson and Seymour, and later joined by Thomas, led to entirely new concepts and a new way of looking at graph theory. The motivating problem was Kuratowski’s characterization of planar graphs, and a far-reaching generalization of this, conjectured by Wagner: If a class of graphs is minor-closed (i.e., it is...

The strong embedding conjecture states that every 2-connected graph has a closed 2-cell embedding in some surface , i . e . an embedding that each face is bounded by a circuit in the graph . A graph is called k -crosscap embeddable if it can be embedded in the surface of non-orientable genus k . We confirm the strong embedding conjecture for 5-crosscap embeddable graphs . As a corollary , every...

Calibrated models of aquifer-system compaction developed by Helm (1975, 1976, 1977, 1978) and by Williamson and others (1989) indicate that a narrow range of both aquitard inelastic skeletal specific storage values and aquitard elastic skeletal specific storage values have been used to successfully simulate aquifersystem compaction despite differences in depth, thickness, lithology, and stratig...