I have opened 
https://trac.sagemath.org/ticket/24683
to, at least, fix the docs.

On Wednesday, February 7, 2018 at 12:27:59 PM UTC, [email protected] wrote:
>
> The main issue is that the hamiltonian path method calls the longest path 
> method.
>
> We should provide a dedicated ILP for hamiltonian path that could 
> optionally search for a hamiltonian path of minimum/maximum cost. 
>
>
> Le mardi 6 février 2018 19:39:32 UTC+1, Dima Pasechnik a écrit :
>>
>>
>>
>> On Tuesday, February 6, 2018 at 5:18:02 PM UTC, Avinandan Das wrote:
>>>
>>> Consider the following :-
>>>
>>> a=[[0, 4, 8], [9, 0, 9], [1000, 1000, 0]]
>>> a=Matrix(a)
>>>  H=DiGraph(a,weighted=True)
>>>  H.hamiltonian_path(used_edge_labels=True)
>>>
>>> This returns (1009, Subgraph of (): Digraph on 3 vertices) but the 
>>> minimum weight Hamiltonian path has weight 13.
>>>
>>
>> Looking at the source code, it seems that it actually returns maximum  
>> weight Hamiltonian path.
>>
>> https://github.com/sagemath/sage/blob/07d6c37d18811e2b377a9689790a7c5e24da16ba/src/sage/graphs/generic_graph.py#L7137
>>
>>
>>
>>
>>
>> I suppose we should amend the documentation.
>>
>>>
>>> I have installed sage-8.1 and my operating system is Ubuntu 14.04 LTS 
>>> (64 bit) and my processor is Intel® Core™ i5-3210M CPU @ 2.50GHz × 4 .
>>>
>>

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