Three Types of Two-Disjoint-Cycle-Cover Pancyclicity and Their Applications to Cycle Embedding in Locally Twisted Cubes
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Abstract A graph $G=(V,E)$ is two-disjoint-cycle-cover $[r_1,r_2]$-pancyclic if for any integer $l$ satisfying $r_1 \leq l \leq r_2$, there exist two vertex-disjoint cycles $C_1$ and $C_2$ in $G$ such that the lengths of $C_1$ and $C_2$ are $l$ and $|V(G)| - l$, respectively, where $|V(G)|$ denotes the total number of vertices in $G$. On the basis of this definition, we further propose Ore-type conditions for graphs to be two-disjoint-cycle-cover vertex/edge $[r_1,r_2]$-pancyclic. In addition, we study cycle embedding in the $n$-dimensional locally twisted cube $LTQ_n$ under the consideration of two-disjoint-cycle-cover vertex/edge pancyclicity.
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2017 ◽
Vol 17
(02)
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pp. 1750006
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2014 ◽
Vol 1049-1050
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pp. 1736-1740
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2012 ◽
Vol 6-7
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pp. 70-75
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2011 ◽
Vol 141
(1-2)
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pp. 1-20
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2014 ◽
Vol 42
(5)
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pp. 351-354
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2009 ◽
Vol 410
(8-10)
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pp. 926-932
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2012 ◽
Vol Vol. 14 no. 2
(Graph Theory)
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