## co.combinatorics – Number of pairs of edge-disjoint Hamilton cycles in complete graphs

Question:
how many pairs $$lbrace H_i, H_jrbrace$$ of edge-disjoint Hamilton cycles are in the complete graph $$K_n$$ with $$n$$ vertices?

while I could find information to the maximal number of edge-disjoint Hamilton cycles in $$K_n$$ I was not able to find anything about the number of combinations $$lbrace H_1,,dots,,H_hrbrace$$, i.e. the number of ways to select $$h$$ edge-disjoint Hamilton cycles from $$K_n$$, specifically for $$h=2$$

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## Graph with two edge-disjoint Hamiltonian paths between the same vertex-pair

Provided existence, what is the smallest graph $$G(V,E)$$ with two edge-disjoint Hamiltonian paths between $$u$$ and $$v; lbrace u,vrbracesubset V$$?

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## relation between steiner tree and Edge-disjoint paths in trees

consider an instance of steiner tree such that at each iteration we connect new required vertex with shortest path to T that T formed previously with this strategy .I want find relate between Edge-disjoint paths in trees and T to find approximation factor logn for steriner tree

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## Edge-disjoint paths in trees – Computer Science Stack Exchange

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Imagine the case where you have two types of currents, say "red" current and "blue" current. You want to send $$k_r$$ red river and $$k_b$$ blue river through a DAG $$G$$ so that no edge carries both red and blue flow. Is there an efficient way to determine if an association of $$k_r$$ red and and $$k_b$$ blue river exists? If so, can it be extended to several "colors"?
An extremely naive solution would be to take any subset of edges $$E & # 39;$$ and check whether you can send or not $$k_r$$ flow through $$G [E & # 39;]$$ and $$k_b$$ flow through $$G [E setminus E & # 39;]$$.