Let P(n, k) denote the number of graphs on n + k vertices that contain Pn, a path on n vertices, as an induced subgraph. In this note we will find upper and lower bounds for P(n, ...
We study approximation algorithms, integrality gaps, and hardness of approximation, of two problems related to cycles of "small" length k in a given graph. The instance f...
Let k be an integer and M be a closed 2-manifold with Euler characteristic (M) 0. We prove that each polyhedral map G on M with minimum degree and large number of vertices conta...
In the NP-hard Cluster Editing problem, we have as input an undirected graph G and an integer k 0. The question is whether we can transform G, by inserting and deleting at most k ...
A simple graph G is k-ordered (respectively, k-ordered hamiltonian) if, for any sequence of k distinct vertices v1, . . . , vk of G, there exists a cycle (respectively, a hamilton...