On approximating the maximum diameter ratio of graphs

On approximating the maximum diameter ratio of graphs

It is proved that computing the maximum diameter ratio also known as the local density of a graph is APX complete The related problem of nding a maximum subgraph of a xed diameter d is proved to be even harder to approximate

On Diameter of Line Graphs

The diameter of a connected graph $G$, denoted by $diam(G)$, is the maximum distance between any pair of vertices of $G$. Let $L(G)$ be the line graph of $G$. We establish necessary and sufficient conditions under which for a given integer $k geq 2$, $diam(L(G)) leq k$.

The maximum genus of diameter three graphs

The maximum gen'us of connected of orient able surface on which G has 2-ce11 C:U.UYC;UUULl.".. to 2,M(G) where (3(G) the Betti n'umber of G.

The omplexity of approximating the oriented diameter of hordal graphs

On the maximum diameter of path-pairable graphs

A graph is path-pairable if for any pairing of its vertices there exist edge disjoint paths joining the vertices in each pair. We obtain sharp bounds on the maximum possible diameter of path-pairable graphs which either have a given number of edges, or are cdegenerate. Along the way we show that a large family of graphs obtained by blowing up a path is path-pairable, which may be of independent...