We study the empire colouring problem (as defined by Percy Heawood in 1890) for maps whose dual planar graph is a tree, with empires formed by exactly r countries. We prove that, ...
The permutation routing problem is studied for trees under the matching model. By introducing a novel and useful (so-called) caterpillar tree partition, we prove that any permutati...
Among the many codings of spanning trees for evolutionary search are those based on bijections between Pr¨ufer strings—strings of n−2 vertex labels—and spanning trees on th...
We consider a class of routing problems on connected graphs G. Initially, each vertex v of G is occupied by a “pebble” which has a unique destination π(v) in G (so that π is...
Arc Routing Problems on mixed graphs have been modelled in the literature either using just one variable per edge or associating to each edge two variables, each one representing ...