In fact, the preview provides the first few sentences of the proof, but then leaves me without the rest! I was interested in this result related to a research direction I was pursuing, but the direction has changed slightly, so admittedly my interest is now purely academic curiosity. Is there a link to the full text of the paper somewhere OR another paper that sketches the proof OR if a proof sketch is short enough to reproduce here, does anyone know it?
Also, I'm interested in the class of graphs with an exponential number of cliques. I think it's a little easier to see this in the complementary form of counting maximal independent sets.
Each maximal independent set has exactly one node from each of these complete subgraphs from which the formula follows. I seem to recall that the upper bound proof of Moon and Moser involved transforming a graph into the lower bound form or the complementary form for maximal cliques , at each step not decreasing the number of independent sets or cliques. But there's a different way of proving it that leads to worst-case-optimal backtracking algorithms for listing all the cliques or independent sets see e. By induction plugging in the formula for the number of independent sets in these two smaller graphs, with some case analysis mod 3 the bound follows.
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On the other hand, if no high degree vertex exists then the graph is a disjoint union of paths and cycles, in which one can calculate the number of independent sets directly. Miller, R. A problem of maximum consistent subsets. Vatter, V. Maximal independent sets and separating covers. American Mathematical Monthly , Wood, D.
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Moon Cliques by Karen T. Smith - Read Online
My question is: Is there a link to the full text of the paper somewhere OR another paper that sketches the proof OR if a proof sketch is short enough to reproduce here, does anyone know it? Cambouropoulos, A.
Smaill, and G. Cambouropoulos and G. Cannings and G. Discrete Algorithms, , pp. Eppstein, Z. Galil, and G. Galil and G. Gardiner, P.
Artymiuk, and P. Gluck and J. Wiley: New York, Henzinger and V. Automata, Languages and Programming, , pp.
Finding All Maximal Cliques in Dynamic Graphs
Johnson and M. Tricks Eds.
http://evromak.ru/modules/viqa-acheter-zithromax.php Li, V. Uren, E. Motta, S. Shum, and J. Moon and L. Motzkin and E. Vickers and C.