Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 3 of 3
Full-Text Articles in Entire DC Network
Continuities On Subspaces, Timothy James Glatzer
Continuities On Subspaces, Timothy James Glatzer
Graduate Theses, Dissertations, and Problem Reports
We define a generalized continuity by declaring that for any family S of subsets of a topological space X, a function f : X → Y is S -continuous if for each S∈ S , the function f ↾ S : S → Y is continuous. This is easily seen to generalize such well known concepts as separate continuity and linear continuity. Using this definition as a way to unify several disparate results, we attempt to create a theory of S -continuity. As a part of this program, we give constructions for S -continuous functions for several natural classes S …
Circuits, Perfect Matchings And Paths In Graphs, Wenliang Tang
Circuits, Perfect Matchings And Paths In Graphs, Wenliang Tang
Graduate Theses, Dissertations, and Problem Reports
We primarily consider the problem of finding a family of circuits to cover a bidgeless graph (mainly on cubic graph) with respect to a given weight function defined on the edge set. The first chapter of this thesis is going to cover all basic concepts and notations will be used and a survey of this topic.;In Chapter two, we shall pay our attention to the Strong Circuit Double Cover Conjecture (SCDC Conjecture). This conjecture was verified for some graphs with special structure. As the complement of two factor in cubic graph, the Berge-Fulkersen Conjecture was introduced right after SCDC Conjecture. …
Connectivity And Spanning Trees Of Graphs, Xiaofeng Gu
Connectivity And Spanning Trees Of Graphs, Xiaofeng Gu
Graduate Theses, Dissertations, and Problem Reports
This dissertation focuses on connectivity, edge connectivity and edge-disjoint spanning trees in graphs and hypergraphs from the following aspects.;1. Eigenvalue aspect. Let lambda2(G) and tau( G) denote the second largest eigenvalue and the maximum number of edge-disjoint spanning trees of a graph G, respectively. Motivated by a question of Seymour on the relationship between eigenvalues of a graph G and bounds of tau(G), Cioaba and Wong conjectured that for any integers d, k ≥ 2 and a d-regular graph G, if lambda 2(G)) < d -- 2k-1d+1 , then tau(G) ≥ k. They proved the conjecture for k = 2, 3, and presented evidence for the cases when k ≥ 4. We propose a more general conjecture that for a graph G with minimum degree delta ≥ 2 k ≥ 4, if lambda2(G) < delta -- 2k-1d+1 then tau(G) ≥ k. We prove the conjecture for k = 2, 3 and provide partial results for k ≥ 4. We also prove that for a graph G with minimum degree delta ≥ k ≥ 2, if lambda2( G) < delta -- 2k-1d +1 , then the edge connectivity is at least k. As corollaries, we investigate the Laplacian and signless Laplacian eigenvalue conditions on tau(G) and edge connectivity.;2. Network reliability aspect. With graphs considered as natural models for many network design problems, edge connectivity kappa'(G) and maximum number of edge-disjoint spanning trees tau(G) of a graph G have been used as measures for reliability and strength in communication networks modeled as graph G. Let kappa'(G) = max{lcub}kappa'(H) : H is a subgraph of G{rcub}. We present: (i) For each integer k > 0, a characterization for graphs G with the property that kappa'(G) ≤ k but for any additional …