Abstract
We study the cut vertex transit function of a connected graph G and discuss its betweenness properties. We show that the cut vertex transit function can be realized as the interval function of a block graph and derive an axiomatic characterization of the cut vertex transit function. We then consider a natural generalization to hypergraphs and identify necessary conditions.
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Acknowledgments
This research work was performed while MC was visiting the Max Plank Institute for Mathematics in the Sciences (MPI-MIS), Leipzig and Leipzig University’s Interdisciplinary Center for Bioinformatics (IZBI). MC acknowledges the financial support of the MPI-MIS, the hospitality of the IZBI, and the Commission for Developing Countries of the International Mathematical Union (CDC-IMU) for providing the individual travel fellowship supporting the research visit to Leipzig. This work was supported in part by SERB-DST, Ministry of Science and Technology, Govt. of India, under the MATRICS scheme for the research grant titled “Axiomatics of Betweenness in Discrete Structures” (File: MTR/2017/000238).
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Changat, M., Nezhad, F.H., Stadler, P.F. (2021). Cut Vertex Transit Functions of Hypergraphs. In: Mudgal, A., Subramanian, C.R. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2021. Lecture Notes in Computer Science(), vol 12601. Springer, Cham. https://doi.org/10.1007/978-3-030-67899-9_17
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