A graph
G is two-disjoint-cycle-cover
r-pancyclic if for any integer
l satisfying
r≤
l≤
|V(
G)
|-
r, there exist two vertex-disjoint cycles
C1 and
C2 in
G such that the lengths of
C1 and
C2 are
|V(
G)
|-
l and
l, respectively, where
|V(
G)
| denotes the total number of vertices in
G. In particular, the graph
G is two-disjoint-cycle-cover vertex
r-pancyclic if for any two distinct vertices
u and
v of
G, there exist two vertex-disjoint cycles
C1 and
C2 in
G such that (i)
C1 contains
u, (ii)
C2 contains
v, and (iii) the lengths of
C1 and
C2 are
|V(
G)
|-
l and
l, respectively, for any integer
l satisfying
r≤
l≤
|V(
G)
|-
r. Moreover,
G is two-disjoint-cycle-cover edge
r-pancyclic if for any two vertex-disjoint edges (
u,
v) and (
x,
y) of
G, there exist two vertex-disjoint cycles
C1 and
C2 in
G such that (i)
C1 contains (
u,
v), (ii)
C2 contains (
x,
y), and (iii) the lengths of
C1 and
C2 are
|V(
G)
|-
l and
l, respectively, for any integer
l satisfying
r≤
l≤
|V(
G)
|-
r. In this paper, we first give Dirac-type sufficient conditions for general graphs to be two-disjoint-cycle-cover vertex/edge 3-pancyclic, and we also prove that the
n-dimensional crossed cube
CQn is two-disjoint-cycle-cover 4-pancyclic for
n≥3, vertex 4-pancyclic for
n≥5, and edge 6-pancyclic for
n≥5.
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