In 1952 Sholander formulated an axiomatic characterization of the interval function of a tree with a partial proof. In 2011 Chvátal et al. gave a completion of this proof. In this paper we present a characterization of the interval function of a block graph using axioms on an arbitrary transit function R. From this we deduce two new characterizations of the interval function of a tree.

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Keywords Block graph, Interval function, Transit function, Tree
Persistent URL dx.doi.org/10.1016/j.disc.2015.01.004, hdl.handle.net/1765/85999
Journal Discrete Mathematics
Citation
Balakrishnan, K, Changat, M, Lakshmikuttyamma, A.K, Mathew, J, Mulder, H.M, Narasimha-Shenoi, P.G, & Narayanan, N. (2015). Axiomatic characterization of the interval function of a block graph. Discrete Mathematics, 338(6), 885–894. doi:10.1016/j.disc.2015.01.004