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Results tagged with hamiltonian-graphs
Search options questions only
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user 12481
A Hamiltonian graph (directed or undirected) is a graph that contains a Hamiltonian cycle, that is, a cycle that visits every vertex exactly once.
5
votes
1
answer
277
views
Infinitely many counterexamples to Nash-Williams's conjecture about hamiltonicity?
Question from 2013
gives one counterexample to Nash-Williams's conjecture about hamiltonicity
of dense digraphs.
Later, we found tens of counterexamples on more than 30 vertices
and believe there are …
- 25.4k
2
votes
0
answers
116
views
Two more counterexamples to a conjecture from 1975 about hamiltonicity of digraphs
Question from 2013
gives one counterexample to Nash-Williams's conjecture 1975 about hamiltonicity
of dense digraphs.
In the linked answer, @LouisD "reverse engineered" the counterexample
and pointed …
- 25.4k
16
votes
1
answer
696
views
A counterexample to a conjecture of Nash-Williams about hamiltonicity of digraphs?
Maybe I am missing something, but found potential counterexample to a conjecture
of Nash-Williams.
According to HAMILTONIAN DEGREE SEQUENCES IN DIGRAPHS
The outdegree and indegree sequences of digr …
- 1,701
1
vote
1
answer
178
views
Is Hamiltonian cycle fixed parameter tractable with parameter clique cover?
Let $G$ be connected simple graph.
Clique cover of graph $G$ is partition of the vertices of $G$
into $k$ disjoint cliques $D'_i$.
Given $G$ and $k$-clique cover, can we solve Hamiltonian cycle
in …
- 196
1
vote
1
answer
78
views
Graph gadget related to uniquely hamiltionian regular graphs (question #2)
Related to uniquely hamiltionian graphs.
For natural numbers $a,b$ define $(a,b)$ gadget $G$:
$G$ is finite simple graph. Two vertices $u,v$ are of degree $b$
and the rest of the vertices are of degre …
CommunityBot
- 1
5
votes
0
answers
93
views
Graph gadget related to uniquely hamiltionian regular graphs
A graph is uniquely hamiltonian if it has exactly one hamiltonian cycle.
According to a conjecture there are no $r$-regular uniquely hamiltonian
graphs for $r > 2$ and of special interest is the case …
- 25.4k
3
votes
1
answer
216
views
Regular graphs with $a$ and $b$ Hamiltonian edges
Special case of this question.
Let $G$ be $r$-regular Hamiltonian graph.
An $a$ edge is an edge which is on every Hamiltonian cycle.
A $b$ edge is an edge which is on no Hamiltonian cycle.
$a(G)$ an …
CommunityBot
- 1