Cost spanning tree problems concern the construction of a tree which provides a connection with the source for every node of the network. In this paper, we address cost sharing problems associated to these situations when the agents located at the nodes act in a non-cooperative way. A class of...

We consider the problem of finding a "fair" or "acceptable" spanning tree in an undirected graph when each member of a group of agents proposes a spanning tree. An "acceptable" spanning tree in that respect is a spanning tree which does not differ in more than a given number of edges from each...

In this paper we take into account three different spanning tree problems with degree-dependent objective functions. The main application of these problems is in the field of optical network design. In particular, we propose the classical Minimum Leaves Spanning Tree problem as a relevant...

Among a variety of subgraphs, spanning trees are one of the most important and fundamental categories. They are relevant to diverse aspects of networks, including reliability, transport, self-organized criticality, loop-erased random walks and so on. In this paper, we introduce a family of...

In this paper we give an exact analytical expression for the number of spanning trees of an infinite family of outerplanar, small-world and self-similar graphs. This number is an important graph invariant related to different topological and dynamic properties of the graph, such as its...

We apply the renormalization group approach to the sandpile on the triangular lattice. The only attractive fixed point is found. The obtained fixed point height probabilities are compared with numerical simulations. The value of critical exponent of avalanche size distribution is found to be τ...

The bi-objective minimum diameter-cost spanning tree problem (bi-MDCST) seeks spanning trees with minimum total cost and minimum diameter. The bi-objective version generalizes the well-known bounded diameter minimum spanning tree problem. The bi-MDCST is a NP-hard problem and models several...