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https://hdl.handle.net/2142/86874
Description
Title
Some Problems in Structural Graph Theory
Author(s)
Cao, Weiting
Issue Date
2006
Doctoral Committee Chair(s)
West, Douglas B.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
For a complete bipartite graph Ks,t, the total number of edges st may not be a triangular number; that is, there may exist 0 < ℓ ≤ n such that e(G) = 1 + 2 + 3 + ··· + n + ℓ. A new question is, can we still decompose the graph Ks,t into distinct paths of lengths 1, 2, 3,..., n, ℓ, one for each, if the necessary condition n ≤ 2t is satisfied? We give a positive answer.
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