1 research outputs found
Silver block intersection graphs of Steiner 2-designs
For a block design , a series of {\sf block intersection graphs}
, or -{\rm BIG}(), is defined in which the
vertices are the blocks of , with two vertices adjacent if and only if
the corresponding blocks intersect in exactly elements. A silver graph
is defined with respect to a maximum independent set of , called a {\sf
diagonal} of that graph. Let be -regular and be a proper -coloring of . A vertex in is said to be {\sf rainbow} with
respect to if every color appears in the closed neighborhood . Given a diagonal of , a coloring is said to be silver
with respect to if every is rainbow with respect to . We say
is {\sf silver} if it admits a silver coloring with respect to some .
We investigate conditions for 0-{\rm BIG}() and 1-{\rm
BIG}() of Steiner systems to be silver