Nonseparating Cycles Avoiding Specific Vertices

A 9k Kernel for Nonseparating Independent Set in Planar Graphs

We study kernelization (a kind of efficient preprocessing) for NP-hard problems on planar graphs. Our main result is a kernel of size at most 9k vertices for the Planar Maximum Nonseparating Independent Set problem. A direct consequence of this result is that Planar Connected Vertex Cover has no kernel with at most (9/8 − ǫ)k vertices, for any ǫ > 0, assuming P 6= NP. We also show a very simple...

Nonseparating vertices in tournaments with large minimum degree

On the number of nonseparating vertices in strongly connected local tournaments

Graph Connectivity After Path Removal

Let G be a graph and u, v be two distinct vertices of G. A u−v path P is called nonseparating if G − V (P ) is connected. The purpose of this paper is to study the number of nonseparating u− v path for two arbitrary vertices u and v of a given graph. For a positive integer k, we will show that there is a minimum integer α(k) so that if G is an α(k)-connected graph and u and v are two arbitrary ...

Shortest Co-cycle Bases of Graphs

In this paper we investigate the structure of the shortest co-cycle base(or SCB in short) of connected graphs, which are related with map geometries, i.e., Smarandache 2dimensional manifolds. By using a Hall type theorem for base transformation, we show that the shortest co-cycle bases have the same structure (there is a 1-1 correspondence between two shortest co-cycle bases such that the corre...