Bounding the Number of Graphs Containing Very Long Induced Paths
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 c...
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| Format: | Others |
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BYU ScholarsArchive
2003
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| Online Access: | https://scholarsarchive.byu.edu/etd/31 https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=1030&context=etd |
| Summary: | 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!). |
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