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Families of locally separated Hamilton paths
Author(s) -
Körner János,
Monti Angelo
Publication year - 2018
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.22220
Subject(s) - combinatorics , mathematics , cardinality (data modeling) , exponential function , upper and lower bounds , graph , discrete mathematics , computer science , mathematical analysis , data mining
We improve by an exponential factor the lower bound of Körner and Muzi for the cardinality of the largest family of Hamilton paths in a complete graph of n vertices in which the union of any two paths has maximum degree 4. The improvement is through an explicit construction while the previous bound was obtained by a greedy algorithm. We solve a similar problem for permutations up to an exponential factor.