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Transforming trees by successive local complementations
Author(s) -
Bouchet André
Publication year - 1988
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.3190120210
Subject(s) - mathematics , combinatorics , conjecture , vertex (graph theory) , graph , discrete mathematics
A local complementation of a simple graph G at a vertex v consists in replacing the subgraph induced by G on the neighborhood of v by the complementary graph. Two graphs are locally equivalent if they are related by a sequence of local complementations. H. M. Mulder conjectured that any two locally equivalent trees are isomorphic. We prove this conjecture and we characterize those graphs that are locally equivalent to trees.