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2015 ; 80
(4
): 287-298
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Monochromatic Clique Decompositions of Graphs
#MMPMID28615799
Liu H
; Pikhurko O
; Sousa T
J Graph Theory
2015[Dec]; 80
(4
): 287-298
PMID28615799
show ga
Let G be a graph whose edges are colored with k colors, and H=(H1,?,Hk) be a
k-tuple of graphs. 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 copy of Hi in color i, for some 1?i?k. Let ?k(n,H) be the smallest
number ?, such that, for every order-n graph and every k-edge-coloring, there is
a monochromatic H-decomposition with at most ? elements. Extending the previous
results of Liu and Sousa [Monochromatic Kr-decompositions of graphs, J Graph
Theory 76 (2014), 89-100], we solve this problem when each graph in H is a clique
and n?n0(H) is sufficiently large.