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Zbl 1166.05019
Mulder, Henry Martyn
Transit functions on graphs (and posets). (English)
[A] Changat, Manoj (ed.) et al., Convexity in discrete structures. Joint proceedings of the international instructional workshop on convexity in discrete structures, Thiruvananthapuram, Kerala, India, March 22--April 2, 2006 and the international workshop on metric and convex graph theory, Barcelona, Spain, June 12--16, 2006. Mysore: Ramanujan Mathematical Society. Ramanujan Mathematical Society Lecture Notes Series 5, 117-130 (2008). ISBN 978-81-902545-5-7/hbk

Summary: The notion of transit function is introduced to present a unifying approach for results and ideas on intervals, convexities and betweenness in graphs and posets. Prime examples of such transit functions are the interval function $I$ and the induced path function $J$ of a connected graph. Another transit function is the all-paths function. New transit functions are introduced, such as the cut-vertex transit function and the longest path function. The main idea of transit functions is that of `transferring' problems and ideas of one transit function to the other. For instance, a result on the interval function $I$ might suggest similar problems for the induced path function $J$. Examples are given of how fruitful this transfer can be. A list of prototype problems and questions for this transferring process is given, which suggests many new questions and open problems.

MSC 2000:: *05C99 Graph theory
05C12 Distance in graphs
05C38 Paths and cycles
05C75 Structural characterization of types of graphs

Keywords: transit function; interval function; induced path; convexity; betweenness; path function; block graph

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