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