4 research outputs found
Transit functions on graphs (and posets)
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 cutvertex
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