AbstractWe prove that if G is a 3-connected plane graph of order p, maximum face length l and radius rad(G), then the bound rad(G)≤p6+5l6+23 holds. For constant l, our bound is shown to be asymptotically sharp and improves on a bound by Harant (1990) [6]. Furthermore we extend these results to 4- and 5-connected planar graphs
International audienceWe show that the diameter $D(G_n)$ of a random (unembedded) labelled connected...
AbstractWe give lower bounds on the length of a longest cycle in a planar graph on n vertices which ...
We show that any face hitting set of size n of a connected planar graph with a minimum degree of at...
AbstractVizing established an upper bound on the size of a graph of given order and radius. We find ...
In graph theory, the degree diameter problem asks for the maximum number of vertices a graph with gi...
AbstractIt is well known that the spectral radius of a tree whose maximum degree is Δ cannot exceed ...
AbstractWe prove that every 3-connected planar graph G of order at least k contains a connected subg...
AbstractWe offer the exact solution of the degree–diameter problem for planar graphs in the case of ...
AbstractWe give asymptotically sharp upper bounds for the maximum diameter and radius of (i) a conne...
summary:In this paper it is proved that every $3$-connected planar graph contains a path on $3$ vert...
AbstractWe prove sharp bounds concerning domination number, radius, order and minimum degree of a gr...
We show that if G is a 3-vertex-connected C4-free graph of order n and radius r, then the inequality...
AbstractWe consider the problem of determining the maximum number of vertices in a planar graph with...
AbstractLet G be any 3-connected graph containing n vertices and r the radius of G. Then the inequal...
AbstractA decomposition result for planar graphs is used to prove that the spectral radius of a plan...
International audienceWe show that the diameter $D(G_n)$ of a random (unembedded) labelled connected...
AbstractWe give lower bounds on the length of a longest cycle in a planar graph on n vertices which ...
We show that any face hitting set of size n of a connected planar graph with a minimum degree of at...
AbstractVizing established an upper bound on the size of a graph of given order and radius. We find ...
In graph theory, the degree diameter problem asks for the maximum number of vertices a graph with gi...
AbstractIt is well known that the spectral radius of a tree whose maximum degree is Δ cannot exceed ...
AbstractWe prove that every 3-connected planar graph G of order at least k contains a connected subg...
AbstractWe offer the exact solution of the degree–diameter problem for planar graphs in the case of ...
AbstractWe give asymptotically sharp upper bounds for the maximum diameter and radius of (i) a conne...
summary:In this paper it is proved that every $3$-connected planar graph contains a path on $3$ vert...
AbstractWe prove sharp bounds concerning domination number, radius, order and minimum degree of a gr...
We show that if G is a 3-vertex-connected C4-free graph of order n and radius r, then the inequality...
AbstractWe consider the problem of determining the maximum number of vertices in a planar graph with...
AbstractLet G be any 3-connected graph containing n vertices and r the radius of G. Then the inequal...
AbstractA decomposition result for planar graphs is used to prove that the spectral radius of a plan...
International audienceWe show that the diameter $D(G_n)$ of a random (unembedded) labelled connected...
AbstractWe give lower bounds on the length of a longest cycle in a planar graph on n vertices which ...
We show that any face hitting set of size n of a connected planar graph with a minimum degree of at...
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