Spanning trees of three-polytopal graphs.

Title: Spanning trees of three-polytopal graphs.
Identifier: AAI9315466
identifier: 9315466
Creator: Hom, Susan.
Contributor: Adviser: Joseph Malkevitch
Date: 1993
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: A 3-polytopal graph is an edge-vertex graph of a convex 3-dimensional polytope. Let G be a 3-valent 3-polytopal graph with no homeomorphically irreducible spanning tree (HIST), i.e, spanning tree without 2-valent vertices. It is shown that an "extension graph" G*, which is constructed from G, has a HIST.;There is a 3-valent 3-polytopal graph G with:V(G): vertices having spanning tree T, whose complement realizes (with some exceptions) any path vector P (cycle vector C; cycle path vector C/P) with entries whose sum is m =:V(G):/2 + 1.;For small number of vertices, there are 3-valent 3-polytopal graphs having spanning trees which realize all possible cycle and cycle/path partitions of m in their complements. However it can be shown that for large numbers of vertices such graphs do not exist. Finally, the case of path partitions is studied.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.