mathematical field of graph theory, a graph G is said to be hypohamiltonian if G itself does not have a Hamiltonian cycle but every graph formed by removing...

The Wiener–Araya graph is, in graph theory, a graph on 42 vertices with 67 edges. It is hypohamiltonian, which means that it does not itself have a Hamiltonian...

deleting a single vertex does have the property. For instance, a hypohamiltonian graph is one that does not have a Hamiltonian cycle, but for which every...

is hypohamiltonian, meaning that although it has no Hamiltonian cycle, deleting any vertex makes it Hamiltonian, and is the smallest hypohamiltonian graph...

planar graphs to have a Hamiltonian cycle Hamiltonian path problem, the computational problem of finding Hamiltonian paths Hypohamiltonian graph, a non-Hamiltonian...

graph is, in graph theory, a hypohamiltonian graph with 16 vertices and 27 edges. It has book thickness 3 and queue number 2. Hypohamiltonian graphs were...

the sense that they are hypohamiltonian graphs: the removal of any single vertex leaves a Hamiltonian subgraph. A hypohamiltonian snark must be bicritical:...

snark J5 is hypohamiltonian. J3 is a trivial variation of the Petersen graph formed by replacing one of its vertices by a triangle. This graph is also known...

with no cycles of length shorter than 5. Chapter seven is on hypohamiltonian graphs, the graphs that do not have a Hamiltonian cycle through all vertices...

and queue number 2. The Coxeter graph is hypohamiltonian: it does not itself have a Hamiltonian cycle but every graph formed by removing a single vertex...

Grinberg's theorem, the graph cannot be Hamiltonian. Grinberg's theorem has also been used to find planar hypohamiltonian graphs, graphs that are not Hamiltonian...

decompositions of cubic graphs". Bull. Austral. Math. Soc. 8 (3): 367–387. doi:10.1017/S0004972700042660. Weisstein, Eric W. "Hypohamiltonian Graph". MathWorld....

221–239, doi:10.2307/2319844, JSTOR 2319844 Weisstein, Eric W. "Hypohamiltonian Graph". MathWorld. Wolz, Jessica; Engineering Linear Layouts with SAT...

the Petersen graph, Tietze's graph is not hypohamiltonian: removing one of its three triangle vertices forms a smaller graph that remains non-Hamiltonian...

is even and k is odd. G(n, k) is a Cayley graph if and only if k2 ≡ 1 (mod n). G(n, k) is hypohamiltonian when n is congruent to 5 modulo 6 and k = 2...

Mohar: Graphs on surfaces, Johns Hopkins University Press 2001 5-choosability of planar graphs (see List coloring) works on Hypohamiltonian graphs Hamilton...

number 3, diameter 4 and girth 5. They are non-hamiltonian but are hypohamiltonian. Both have book thickness 3 and queue number 2. The automorphism group...

Bondy's theorem Bondy–Chvátal theorem Even circuit theorem Hypohamiltonian graph Pancyclic graph John Adrian Bondy at the Mathematics Genealogy Project Charbit...