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Please use this identifier to cite or link to this item: http://hdl.handle.net/10210/209128

- roleTerm (text)
- advisor
- namePart
- Prof. I. Broere
- roleTerm (text)
- author
- namePart
- Jonck, Elizabeth
- dateAccessioned
- 2012-09-06T12:52:43Z
- dateAvailable
- 2012-09-06T12:52:43Z
- dateIssued
- 2012-09-06
- dateSubmitted
- 1997
- identifier (uri)
- http://hdl.handle.net/10210/7118
- note
- Ph.D.
- abstract
- The induced path number p(G) of a graph G is defined as the minimum number of subsets into which the vertex set V(G) of G can be partitioned such that each subset induces a path. In this thesis we determine the induced path number of a complete £-partite graph. We investigate the induced path number of products of complete graphs, of the complement of such products and of products of cycles. For a graph G, the linear vertex arboricity lva(G) is defined as the minimum number of subsets into which the vertex set of C can be partitioned so that each subset induces a linear forest. Since each path is a linear forest, Iva(G) p(G) for each graph C. A graph G is said to be uniquely rn-li near- forest- partition able if lva(C) = in and there is only one partition of V(G) into m subsets so that each subset induces a linear forest. Furthermore, a graph C is defined to be nz- Iva- saturated if Iva(G) < in and lva(C + e) > iii for each e E We construct graphs that are uniquely n2-linear-forest-partitionable and in-lva-saturated. We characterize those graphs that are uniquely m-linear-forest-partitionable and rn-lvasaturated. We also characterize the orders of uniquely in- path- partitionable disconnected, connected and rn-p-saturated graphs. We look at the influence of the addition or deletion of a vertex or an edge on the path partition number. If C is a graph such that p(G) = k and p(G - v) = k - 1 for every v E V(G), then we say that C is k-minus-critical. We prove that if C is a connected graph consisting of cyclic blocks Bi with p(B1 ) = b, for i = 1,2, ... ,n where ii > 2 and k bi - n+ 1, then C is k- minus- critical if and only if each of the blocks B1 is a bj- minus- critical graph.
- languageTerm (rfc3066)
- en
- topic
- Algebra - Graphic methods.
- topic
- Graphic methods - Problems, exercises, etc.
- topic
- Graph theory.
- topic
- Path analysis.
- title
- The path partition number of a graph
- genre
- Thesis

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