<p>A good resource to answer questions like this is graphclasses.org.  You find the graph class you care about -- in this case, <a href="https://www.graphclasses.org/classes/gc_1092.html" rel="nofollow noreferrer">Hamiltonian graphs</a>.  Then check the maximal subclasses section, and possibly forward-search from there.</p>

CC BY-SA 4.0
2021-05-03T15:07:39.310Z
Thanks. That was quite helpful tip.
Vk1
CC BY-SA 4.0
2021-05-03T19:00:32.530Z
All but one of these classes explicitly includes Hamiltonicity in their definition.
Yonatan N
CC BY-SA 4.0
2021-05-03T13:39:39.693Z
2021-05-03T13:39:39.693Z
GMB
<p>One trivial class of graphs is the class consisting of complete graphs or complete bipartite graphs with equal sized partitions.
I would love to know if more such classes exist.</p>

CC BY-SA 4.0
2021-05-02T16:42:00.787Z
The wikipedia article for Hamiltonian path gives some sufficient conditions (mainly the Bondy–Chvátal theorem and special cases as well as the fact that any 4-connected planar graph has a Hamiltonian path).
Tassle
CC BY-SA 4.0
2021-05-02T17:25:21.297Z
I checked the wiki article. The question intends to know about more such classes which have this property.
Vk1
CC BY-SA 4.0
2021-05-03T20:06:16.147Z
It's a (fairly) well-known open question as to whether every Cayley graph is Hamiltonian. [Pak & Radoicic 2008](https://www.math.ucla.edu/~pak/papers/hamcayley9.pdf)
Joshua Grochow
<graph-theory><hamiltonian-paths><graph-classes>
What are the known classes of undirected graphs such that every graph belonging to that class is guaranteed to have a Hamiltonian Path?
Vk1
# What are the known classes of undirected graphs such that every graph belonging to that class is guaranteed to have a Hamiltonian Path?

(Asked by: username_0 on 2021-05-02)

One trivial class of graphs is the class consisting of complete graphs or complete bipartite graphs with equal sized partitions.
I would love to know if more such classes exist.

**Tags:** graph-theory, hamiltonian-paths, graph-classes
> **Comments:**
> **username_1**: The wikipedia article for Hamiltonian path gives some sufficient conditions (mainly the Bondy–Chvátal theorem and special cases as well as the fact that any 4-connected planar graph has a Hamiltonian path).  
> **username_0**: I checked the wiki article. The question intends to know about more such classes which have this property.  
> **username_2**: It's a (fairly) well-known open question as to whether every Cayley graph is Hamiltonian. [Pak & Radoicic 2008](https://www.math.ucla.edu/~pak/papers/hamcayley9.pdf)  

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## 1 answers

### Answer by username_3 on 2021-05-03. Score: 3

A good resource to answer questions like this is graphclasses.org. You find the graph class you care about -- in this case, [Hamiltonian graphs](https://www.graphclasses.org/classes/gc_1092.html). Then check the maximal subclasses section, and possibly forward-search from there.

> **Comments:**
> **username_0**: Thanks. That was quite helpful tip.  
> **username_4**: All but one of these classes explicitly includes Hamiltonicity in their definition.  

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