Abstract
Induced graphs are used to describe the structure of a graph, one such type of induced graph that has been studied are long paths.
In this thesis we show a way to represent such graphs in terms of an array with two colors and a labeled graph. Using this representation and the techniques of Polya counting we will then be able to get upper and lower bounds for graphs containing a long path as an induced subgraph.
In particular, if we let P(n,k) be the number of graphs on n+k vertices which contains P_n, a path on n vertices, as an induced subgraph then using our upper and lower bounds for P(n,k) we will show that for any fixed value of k that P(n,k)~2^(nk+k_C_2)/(2k!).
Degree
MS
College and Department
Physical and Mathematical Sciences; Mathematics
Rights
http://lib.byu.edu/about/copyright/
BYU ScholarsArchive Citation
Butler, Steven Kay, "Bounding the Number of Graphs Containing Very Long Induced Paths" (2003). Theses and Dissertations. 31.
https://scholarsarchive.byu.edu/etd/31
Date Submitted
2003-02-07
Document Type
Thesis
Handle
http://hdl.lib.byu.edu/1877/etd158
Keywords
mathematics, combinatorics, graph theory, paths, induced paths, asymptotic behavior, stirling numbers, polya counting, Burnsides theorem
Language
English