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Cartesian products of trees and paths
Author(s) -
Bandelt HansJürgen,
Burosch Gustav,
Laborde JeanMarie
Publication year - 1996
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/(sici)1097-0118(199608)22:4<347::aid-jgt8>3.0.co;2-l
Subject(s) - cartesian product , mathematics , combinatorics , vertex (graph theory) , product (mathematics) , tree (set theory) , regular polygon , cartesian coordinate system , characterization (materials science) , discrete mathematics , graph , geometry , materials science , nanotechnology
We characterize the (weak) Cartesian products of trees among median graphs by a forbidden 5‐vertex convex subgraph. The number of tree factors (if finite) is half the length of a largest isometric cycle. Then a characterization of Cartesian products of n trees obtains in terms of isometric cycles and intervals. Finally we investigate to what extent the proper intervals determine the product structure. © 1996 John Wiley & Sons, Inc.