A tabu random walk on a graph is a partially self-avoiding random walk which uses a bounded memory to avoid cycles. This memory is called a tabu list and contains vertices already visited by the walker. The size of the tabu list being bounded, the way vertices are inserted and removed from the list, called here an update rule, has an important impact on the… (More)
A tabu random walk on a graph is a partially self-avoiding random walk to nearest neighbors with finite memory. The walker is endowed with a finite word, called tabu list, whose letters are vertices he has already visited. The policy to insert or remove occurrences of vertices in the tabu list is called update rule. First, we enunciate a necessary and… (More)
Consider the random walk on graphs such that, at each step, the next visited vertex is a neighbor of the current vertex, chosen with probability proportional to the inverse of the square root of its degree. On one hand, for every graph with n vertices, the maximal mean hitting time for this degree-biased random walk is asymptotically dominated by n 2. On… (More)
/Résumé We prove that two disjoint graphs must always be drawn separately on the Klein bottle in order to minimize the crossing number of the whole drawing. Dans ce rapport, nous prouvons que deux graphes disjoints doivent toujoursêtre dessinés séparément sur la bouteille de Klein lorsque le nombre de croisements du dessin est minimal.