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Monochromatic K r ‐Decompositions of Graphs
Author(s) -
Liu Henry,
Sousa Teresa
Publication year - 2014
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.21750
Subject(s) - monochromatic color , combinatorics , mathematics , partition (number theory) , graph , discrete mathematics , physics , optics
Given graphs G and H , and a coloring of the edges of G with k colors, a monochromatic H‐decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a monochromatic graph isomorphic to H . Letϕ k ( n , H )be the smallest number ϕ such that any graph G of order n and any coloring of its edges with k colors, admits a monochromatic H ‐decomposition with at most ϕ parts. Here, we study the functionϕ k ( n , K r )for k ≥ 2 and r ≥ 3 .