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Minimum cycle bases for direct products of K2 with complete graphs
(
University of Queensland Press
, 2009 , Article)
We construct a minimum cycle basis for the direct product K2 x Kp of two complete graphs where p > 2. For p > 3, these bases consists only of squares. This completes the work of R. Hammack, who treated the case Kp x ...
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
. ...
The cycle-complete graph Ramsey number r(C6,K8)≤38
(
Tokyo University of Science
, 2008 , 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
. ...