G-2013-83
A Note on r-Equitable k-Colorings of Trees
and BibTeX reference
A graph G=(V,E)
is r
-equitably k
-colorable if there exists a partition of V
into k
independent
sets V1,V2,…,Vk
such that ||Vi|−|Vj||≤r
for all i,j∈{1,2,…,k}
. In this note, we show that if two
trees T1
and T2
of order at least two are r
-equitably k
-colorable for r≥1
and k≥3
, then all trees obtained
by adding an arbitrary edge between T1
and T2
are also r
-equitably k
-colorable.
Published November 2013 , 8 pages
Research Axis
Publication
Jan 2014
and
YUJOR, 24(2), 293–298, 2014
BibTeX reference