Clique Polynomials Part 2 - Deeper Look [Graph Theory Tutorial]
In this video we cover clique polynomials in-depth, proving some major theorems relating to clique polynomials. Specifically, we prove a theorem relating the maximum real roots of clique polynomials of spanning subgraphs to those of the original graph. This theorem lets us establish new criteria for Hamiltonian cycles in graphs. Clique polynomials were examined deeply in Hajbolhassan and Merabadi's 1998 paper on clique polynomials, available at this link: https://citeseerx.ist.psu.edu/viewdoc...
Here are some more links for further exploration:
https://mathworld.wolfram.com/CliqueP...
https://arxiv.org/abs/1910.11196
https://www.jstor.org/stable/43666386...
https://www.researchgate.net/publicat...
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