Herschel graph en · PROPN
Etymology
From Herschel (“a surname”) + graph, after British astronomer Alexander Stewart Herschel (1836–1907), who identified the associated polyhedron (an enneahedron) as one for which there is no solution to the icosian game.
Meanings
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A bipartite undirected graph with 11 vertices and 18 edges that is the smallest non-Hamiltonian polyhedral graph.
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.
1994, Ralph P. Grimaldi, Discrete and Combinatorial Mathematics: An Applied Introduction, page 587:2006, 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.
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.
2004, William Kocay, Donald L. Kreher, Graphs, Algorithms, and Optimization, page 202:
Synonyms
Herschel's graph (smallest non-Hamiltonian polyhedral graph)
wikipedia: icosian game · wikipedia: Alexander Stewart Herschel