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Group divisible ( K 4 − e ) ‐packings with any minimum leave
Author(s) -
Gao Yufeng,
Chang Yanxun,
Feng Tao
Publication year - 2018
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21600
Subject(s) - combinatorics , mathematics , graph , disjoint sets , group (periodic table) , discrete mathematics , organic chemistry , chemistry
A decomposition ofK n ( g ) ∖ L , the complete n ‐partite equipartite graph with a subgraph L (called the leave) removed, into edge disjoint copies of a graph G is called a maximum group divisible packing of K n ( g )with G if L contains as few edges as possible. We examine all possible minimum leaves for maximum group divisible ( K 4 − e ) ‐packings. Necessary and sufficient conditions are established for their existences.