Author Type

Graduate Student

Date of Award

1991

Document Type

Thesis

Publication Status

Version of Record

Submission Date

October 2026

Thesis/Dissertation Advisor [Chair]

Locke, Stephen C.

Abstract

A cycle double cover (CDC) of a graph G is a collection C of cycles of G such that each edge of G belongs to exactly two members of C. P. D. Seymour conjectured that every 2-edge-connected graph admits a CDC. In a similar way, a path double cover (PDC) of graph G is a collection P of paths of G such that each edge of G belongs to exactly two paths of P. If each vertex of G is an end of exactly two paths of P, then P is called a perfect path double cover (PPDC). J. A. Bondy asked if every simple graph admits a PPDC. In the first part of this thesis, we present some techniques that have been applied to the cycle double cover conjecture and give a detailed study of CDC for some particular graphs. It has been found that this conjecture is true of planar graphs, 3-edge-colorable cubic graphs, Cayley graphs and graphs which have a Hamiltonian path. In the second part of this thesis, we mainly deal with path double covers and their variants. We will see that every simple graph admits a PPDC and the PPDC problem is in class P. A detailed summary about the main results discussed in this thesis is included.

Extent

89 p.

Comments

Thesis (M.S.)--Florida Atlantic University, 1991.|Thesis (M.S.)--Florida Atlantic University, 1991.

Identifier

FADT14687

Format

pdf

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