The question of whether there is a logic that captures polynomial time was formulated by Yuri Gurevich in 1988. It is still wide open and regarded as one of the main open problems...
In this paper we study the cycle base structures of embedded graphs on surfaces. We first give a sufficient and necessary condition for a set of facial cycles to be contained in ...
Let G be the set of finite graphs whose vertices belong to some fixed countable set, and let ≡ be an equivalence relation on G. By the strengthening of ≡ we mean an equivalen...
We prove new results on evasiveness of monotone graph properties by extending the techniques of Kahn, Saks, and Sturtevant [Combinatorica, 4 (1984), pp. 297–306]. For the propert...
We consider graphs such as the minimum spanning tree, minimum Steiner tree, minimum matching, and traveling salesman tour for n points in the d-dimensional unit cube. For each of ...