A New Chvátal Type Condition for Pancyclicity

A neighbourhood union condition for pancyclicity

Pancyclicity of Hamiltonian and highly connected graphs

A graph G on n vertices is Hamiltonian if it contains a cycle of length n and pancyclic if it contains cycles of length ` for all 3 ≤ ` ≤ n. Write α(G) for the independence number of G, i.e. the size of the largest subset of the vertex set that does not contain an edge, and κ(G) for the (vertex) connectivity, i.e. the size of the smallest subset of the vertex set that can be deleted to obtain a...

The Existence of a 2-Factor in a Graph Satisfying the Local Chvátal-Erdös Condition

The well-known Chvátal–Erdős Theorem states that every graph G of order at least three with α(G) ≤ κ(G) has a hamiltonian cycle, where α(G) and κ(G) are the independence number and the connectivity of G, respectively. Oberly and Sumner [J. Graph Theory 3 (1979), 351–356] have proved that every connected, locally-connected claw-free graph of order at least three has a hamiltonian cycle. We study...

Pancyclicity of OTIS (swapped) networks based on properties of the factor graph

a r t i c l e i n f o a b s t r a c t The plausibility of embedding cycles of different lengths in the graphs of a network (known as the pancyclicity property) has important applications in interconnection networks, parallel processing systems, and the implementation of a number of either computational or graph problems such as those used for finding storage schemes of logical data structures, ...

Node-pancyclicity and edge-pancyclicity of hypercube variants

Twisted cubes, crossed cubes, Möbius cubes, and locally twisted cubes are some of the widely studied hypercube variants. The 4-pancyclicity of twisted cubes, crossed cubes, Möbius cubes, locally twisted cubes and the 4-edgepancyclicity of crossed cubes are proven in [2, 1, 5, 10, 6] respectively. It should be noted that 4-edge-pancyclicity implies 4-node-pancyclicity which further implies 4-pan...