We consider the problem of counting the number of spanning trees in planar graphs. We prove tight bounds on the complexity of the problem, both in general and especially in the mo...
It was shown in [11] that any orientable graph of genus g can be probabilistically embedded into a graph of genus g − 1 with constant distortion. Removing handles one by one giv...
Glencora Borradaile, James R. Lee, Anastasios Sidi...
Abstract. We prove that for every graph H, there exists a polynomial-time algorithm deciding if a planar graph can be contracted to H. We introduce contractions and topological min...
In the Planar +k vertex problem the task is to find at most k vertices whose deletion makes the given graph planar. The graphs for which there exists a solution form a minor close...
The linear arboricity la(G) of a graph G is the minimum number of linear forests that partition the edges of G. In 1984, Akiyama et al. [1] stated the Linear Arboricity Conjecture...