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The basis number of the strong product of paths and cycles with bipartite graphs
(
Central Missouri State University
, 2007 , Article)
The basis number of a graph G is defined to be the least integer d such that there is a basis B of the cycle space of G such that each edge of G is contained in at most d members of B. MacLane [13] proved that a graph G ...
The cycle-complete graph Ramsey number r ( C 8 , K 8 )
(
Tokyo University of Science
, 2007 , Article)
The cycle-complete graph Ramsey number
r
(
C
m
,
K
n
)
is the smallest integer
N
such that every graph
G
of order
N
contains a cycle
C
m
on
m
vertices or has independent number
α
(
G
)
≥
n
. ...