Abstract
The intersection preserving mapping problem was introduced by Czimmermann in his research on isomorphism of hypergraphs. This paper explores the condition when an intersection preserving mapping is not induced by any bijection. A new characterization of intersection preserving mappings is presented, and a generalization of Whitney’s line graph isomorphism theorem is proved.
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Czimmermann, P.: Generalisations of hypomorphisms and reconstruction of hypergraphs. Graphs Comb. 32, 1–15 (2015)
Whitney, Hassler: Congruent graphs and the connectivity of graphs. Am. J. Math. 54, 150–168 (1932)
Zou, Y.: The Hypergraph Degree Sequence Problem, M.Sc. thesis, University of Manitoba, Canada (2016)
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This work is partially supported by a discovery grant from the National Science and Engineering Council of Canada.
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Zou, Y., Kocay, W.L. Intersection Preserving Mappings. Graphs and Combinatorics 33, 1081–1087 (2017). https://doi.org/10.1007/s00373-017-1795-2
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DOI: https://doi.org/10.1007/s00373-017-1795-2