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Almost resolvable P k ‐decompositions of complete graphs
Author(s) -
Yu MinLi
Publication year - 1991
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.3190150506
Subject(s) - mathematics , combinatorics , partition (number theory) , vertex (graph theory) , decomposition , discrete mathematics , graph , chemistry , organic chemistry
An almost P k ‐factor of G is a P k ‐factor of G ‐ { v } for some vertex v. An almost resolvable P k ‐decomposition of λ K n is a partition of the edges of λ K n into almost P k ‐factors. We prove that necessary and sufficient conditions for the existence of an almost resolvable P k ‐decomposition of λ K n are n ≡ 1 (mod k) and λnk /2 ≡ 0 (mod k −1).