Martín Cera

Connectivity of graphs with given girth pair

Girth pairs were introduced by Harary and Kovacs [Regular graphs with given girth pair, J. Graph Theory 7 (1983) 209-218]. The odd girth (even girth) of a graph is the length of a shortest odd (even) cycle. Let g denote the smaller of the odd and even girths, and let h denote the larger. Then (g,h) is called the girth pair of the graph. In this paper we prove that a graph with girth pair (g,h) such that g is odd and h>=g+3 is even has high (vertex-)connectivity if its diameter is at most h-3. The edge version of all results is also studied.

The Size of a Graph Without Topological Complete Subgraphs

In this note we show a new upperbound for the function ex(n;TKp), i.e., the maximum number of edges of a graph of order n not containing a subgraph homeomorphic to the complete graph of order p. Further, for

Extremal Graphs without Topological Complete Subgraphs

{\left \lceil \frac{2n+5}{3}\right \rceil}\leq p

An advance in infinite graph models for the analysis of transportation networks

The exact values of the function

Theoretical Progress on Infinite Graphs and Their Average Degree: Applicability to the European Road Transport Network

ex(n;TK_{p})

On the restricted connectivity and superconnectivity in graphs with given girth

are known for

Sufficient conditions for λ′-optimality of graphs with small conditional diameter

{\lceil \frac{2n+5}{3}\rceil}\leq p < n

Diameter-girth sufficient conditions for optimal extraconnectivity in graphs

(see [Cera, Dianez, and Marquez, SIAM J. Discrete Math., 13 (2000), pp. 295--301]), where

On the edge-connectivity and restricted edge-connectivity of a product of graphs

ex(n;TK_p)

Locating a Central Hunter on the Plane

is the maximum number of edges of a graph of order