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Results On Hyperspaces, Jorge M. Martinez-Montejano
Results On Hyperspaces, Jorge M. Martinez-Montejano
Graduate Theses, Dissertations, and Problem Reports
A characterization of Cp(X), the family of subcontinua of X containing a fixed point of X, when X is an atriodic continuum is given as follows. Assume Z is a continuum and consider the following three conditions: (1) Z is a planar absolute retract; (2) cut points of Z have component number two; (3) any true cyclic element of Z contains at most two cut points of Z. If X is an atriodic continuum and p ∈ X, then Cp(X) satisfies (1)--(3) and, conversely, if Z satisfies (1)--(3), then there exist an arc-like continuum (hence, atriodic) X and a point …
Graph Minor, Jianbing Niu
Graph Minor, Jianbing Niu
Graduate Theses, Dissertations, and Problem Reports
In this paper, we present three results: (1) Let G be a (k + 2)-connected non-(k - 3)-apex graph where k ≥ 2. If G contains three k-cliques, say L 1, L2, L3, such that |Li ∩ Lj| ≤ k - 2 (1 ≤ i < j ≤ 3), then G contains a Kk +2 as a minor. (2) Let G be a 6-connected claw-free graph. If delta(G) ≥ 7 and G contains three disjoint 5-cliques, say Ll, L2, L3, then G contains a K7 as a minor. (3) There is a function h : N → N, such that, for every 4-connected graph G with minimum degree at least five embedded in a surface with Euler genus g and face-width at least h(g), every longest circuit of the graph G has a chord.
On Flows Of Graphs, Rui Xu
On Flows Of Graphs, Rui Xu
Graduate Theses, Dissertations, and Problem Reports
Tutte's 3-flow Conjecture, 4-flow Conjecture, and 5-flow Conjecture are among the most fascinating problems in graph theory. In this dissertation, we mainly focus on the nowhere-zero integer flow of graphs, the circular flow of graphs and the bidirected flow of graphs. We confirm Tutte's 3-flow Conjecture for the family of squares of graphs and the family of triangularly connected graphs. In fact, we obtain much stronger results on this conjecture in terms of group connectivity and get the complete characterization of such graphs in those families which do not admit nowhere-zero 3-flows. For the circular flows of graphs, we establish …