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You could look for a sequence of permutations, that are adjacent in the Steinhaus-Johnson-Trotter sequence of permutations http://en.wikipedia.org/wiki/Steinhaus%E2%80%93Johnson%E2%80%93Trotter_algori …

For the algorithmic solution, i.e. reducing the problem to an ordinary matching problem, the following idea helps: every of the $k$ girls has bucket with $n$ balls and every girl also has $n$ empt …

One aspect of exhanging the balls a girl initially has with balls from other girls can be interpreted as an assignment problem, namely matching the balls a girl has with the colors (depicted as square …

Motivated by a recent upvote, I started to reconsider the problem. The first thing I did, was to repeat my search for algorithms that generate the $n$-th Steinhaus-Trotter-Johnson permutation - needle …

the answer is yes, simply because there are at least two different paths for $n\ge 2$. Assuming that at least two different paths exist for $n\ge 2$ one can interpret the 1st path as a $0$bit and the …

Question: how many pairs $\lbrace H_i, H_j\rbrace$ 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-disj …

In their article "Double-Tree Approximations for the Metric TSP: Is the Best One Good Enough?", Vladimir Deineko and Alexander Tiskin derive a lower bound for the approximation ratio of the double-tre …

Question: are Gray Codes known for enumerating all fixed-size subsets of a given finite set? Background of the question is trying to find the lightest k-clique in a symmetric TSP instance of s …

Let $G(V,E)$ be a connected, simple and undirected graph with the additional constraint, that each edge is contained in the same number $k_T$ of triangles; i.e. that $G$ is regular w.r.t. to that numb …

Weighted $K_4$ are the simplest non-trivial symmetric TSP instances that already exhibit a rich variety of properties, e.g. that the shortest edge is not contained in the optimal solution or that the …

are there any invariants of matrices, that are not affected by row- and/or column permutations? To me it seems that the sequence of singular values could be such an invariant; am I right, resp. are t …

Are there deterministic algorithms that generate a sequence of Hamilton Tours that is superior to a sequence of randomly chosen tours, when applied to the TSP (by applying to the TSP, I understand sum …

Let the edge set of a Optimal k-Tour Spanner of a graph $G$ be equal to the edges of $G$ that lie on at least one optimal tour through exactly $3<k<n$ distinct vertices of $G$. I would like to know …

Given: $G:=\{V= \{v_1,\ ...\ v_n\},E\subset V\times V\}, n<\infty$, a symmetric complete, simple graph $w:=\ \ E \ni e_{ij}\mapsto \mathbb{R}^+$, a weight function for the edges of $G$ $K:=\{c_1,\ ... …

There is a fairly rich classification on graphs with respect to the existence of Hamiltonian cycles either in unmodified graphs or after certain small modifications. Do there also exist such classi …