Closure for the property of having a hamiltonian prism

Abstract

Abstract:We prove that a graph G of order n has a hamiltonian prism if and only if the graph Cl 4n/3−4/3 (G) has a hamiltonian prism where Cl 4n/3−4/3 (G) is the graph obtained from G by sequential adding edges between non-adjacent vertices whose degree sum is at least 4n/3 − 4/3. We show that this cannot be improved to less than 4n/3 − 5.

A counterexample to prism-hamiltonicity of 3-connected planar graphs

“…Many classes of graphs are prism-hamiltonian: chordal 3-connected planar graphs (also known as kleetopes) [9], planar near-triangulations [2], Halin graphs [9], line graphs of bridgeless graphs [9], 3-connected cubic graphs [12] and [4], and graphs that fulfil special degree conditions [11]. A characterization of prism-hamiltonian graphs is also given in [10]. Hamiltonicity of k-fold prisms is studied in [13], where the authors prove that for every k ≥ 2 the k-fold prism G2Q k over a 3-connected planar graph G is hamiltonian (here Q k denotes the k-cube).…”