Meaning of Herschel graph | Babel Free

Definitions

A bipartite undirected graph with 11 vertices and 18 edges that is the smallest non-Hamiltonian polyhedral graph.

Examples

“Select⟳ a suitable independent set⟳ / and use⟳ part (b) to show⟳ that the graph in Fig. 11.81 (known as the Herschel graph) has no Hamilton cycle.”

“A bipartite graph like⟳ the Herschel graph of Figure⟳ 9.2 is also non-hamiltonian, but the algorithm is not likely to delete⟳ enough vertices to notice⟳ that it has a large separating set⟳.”

“2006, Michael S. Keane, Dee Denteneer, Frank Hollander, Evgeny Verbitskiy, Dynamics and Stochastics, Institute of Mathematical Statistics, Lecture⟳ Notes—Monograph Series, Volume 48, page 174, It is difficult to control⟳ what loops may arise⟳: for example the Herschel graph [3] shows that a convex polyhedron need⟳ not be Hamiltonian as a graph.”

CEFR level