Posted by admin | Posted in Golf | Posted on 19-05-2010
Tags: design, graph regular, graph regularization, programming, regexp, tools, visualization
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prove that any r-regular graph(r=2k) is hamiltonian.note that the graph is connected.?
There was some stuff about something like this:
(a) Let C be the longest cycle in a graph and suppose there exists a vertex w not onthe cycle. Prove that w cannot have two consecutive neighbors on the cycle.
(b) Pick an orientation on C. Let S denote the set of successors of neighbors of w onC. Show that S is an independent set.
(c) Prove that the above results generalize if we consider internally disjoint pathsfrom w to C rather than just edges.
There’s another paper about digraphs here that might or might not help: http://www.math.cmu.edu/users/af1p/direg.pdf
Trig 2.2 Examples Part 1 Graphs of Equations with Two Variables
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