<abstract xmlns="http://www.w3.org/1999/xhtml"><p> This paper extends to infinite graphs the most general extremal issues, which are problems of determining the maximum number of edges of a graph not containing a given subgraph. It also relates the new results with the corresponding situations for the finite case. In particular, concepts from ‘finite’ graph theory, like the average degree and the extremal number, are generalized and computed for some specific cases. Finally, some applications of infinite graphs to the transportation of dangerous goods are presented; they involve the analysis of networks and percolation thresholds.</p></abstract>

This paper extends to infinite graphs the most general extremal issues, which are problems of determining the maximum number of edges of a graph not containing a given subgraph. It also relates the new results with the corresponding situations for the finite case. In particular, concepts from ‘finite’ graph theory, like the average degree and the extremal number, are generalized and computed for some specific cases. Finally, some applications of infinite graphs to the transportation of dangerous goods are presented; they involve the analysis of networks and percolation thresholds.

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

Department of Applied Mathematics I University of Seville, ETSIA, Ctra. Utrera km 1, ES-41013 Seville,

Department of Economics, Quantitative Methods and Economic History Pablo de Olavide University, Ctra. Utrera km 1, ES-41013 Seville,

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"An advance in infinite graph models for the analysis of transportation networks"}

This paper extends to infinite graphs the most general extremal issues, which are problems of determining the maximum number of edges of a graph not containing...

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

Article Category: Individual Article Information

Published Online: Dec 30, 2016

Page range: 855 - 869

Received: Sep 29, 2015

Accepted: Jul 02, 2016

DOI: https://doi.org/10.1515/amcs-2016-0061

© by Martín Cera

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.