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Results tagged with cycles
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user 9025
3
votes
Counting simple 4-cycles in an undirected graph
The number of 4-cycles is
$$\frac{1}{2}\sum_{\lbrace v,w\rbrace} \binom{c(v,w)}{2},$$
where the sum is over the $\binom{V}{2}$ pairs of vertices and $c(v,w)$ is the number of common neighbours of $v$ and …
- 37.7k
12
votes
Accepted
How many edge-disjoint cycles of length 3 are in the complete graph?
The maximum number of edge-disjoint triangles in a complete graph is determined by:
Joel Spencer.
Maximal consistent families of triples.
J. Combinatorial Theory, 5 1968 1–8.
- 37.7k
2
votes
Need input on a potentially NP-hard maximal edge-weighted multi-cycle graph
For directed graphs, or undirected graphs where edges are treated as cycles of length 2 (so their weight counts twice), it is easy to do it in polynomial time using a maximum matching algorithm. …
- 37.7k