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Codes with structured Hamming distance in graph families

by   Anna Gujgiczer, et al.
Budapest University of Technology and Economics
Renyi Institute of Mathematics
Sapienza University of Rome

We investigate the maximum size of graph families on a common vertex set of cardinality n such that the symmetric difference of the edge sets of any two members of the family satisfies some prescribed condition. We solve the problem completely for infinitely many values of n when the prescribed condition is connectivity or 2-connectivity, Hamiltonicity or the containment of a spanning star. We give lower and upper bounds when it is the containment of some fixed finite graph concentrating mostly on the case when this graph is the 3-cycle or just any odd cycle. The paper ends with a collection of open problems followed by an important update in this new version of the manuscript..


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