Transit functions on graphs (and posets)

Abstract

The notion of transit function is introduced to present a unifying approachfor results and ideas on intervals, convexities and betweenness in graphs andposets. Prime examples of such transit functions are the interval function I andthe induced path function J of a connected graph. Another transit function isthe all-paths function. New transit functions are introduced, such as the cutvertextransit function and the longest path function. The main idea of transitfunctions is that of ‘transferring’ problems and ideas of one transit functionto the other. For instance, a result on the interval function I might suggestsimilar problems for the induced path function J. Examples are given of howfruitful this transfer can be. A list of Prototype Problems and Questions forthis transferring process is given, which suggests many new questions and openproblems.graph theory;betweenness;block graph;convexity;distance in graphs;interval function;path function;induced path;paths and cycles;transit function;types of graphs