Talk:Hamiltonian path

message: The starting paragraph contains a wrong definition. As it is defined now, any graph contains a Hamiltonian path (e.g., the empty path, or a single edge between two vertices). The reason is that it only requires the path to visit each vertex *in the path* once; it doesn't require that each *and every* vertex in the graph is visited!
-- Indeed you are correct. This is an incorrect definition; otherwise, the statement: "Determining whether such paths and cycles exist in graphs is the Hamiltonian path problem, which is NP-complete." is incorrect!
79.66.220.18 (talk) 15:39, 9 May 2017 (UTC)
thread_title:  Incorrect Definition 

message: I separated Hamiltonian path and Hamiltonian path problem. Although they are related, I think it is clearer to put them on separate pages. MathMartin 17:58, 24 Jan 2005 (UTC)
thread_title: Separated article

message: Some authors (notably, Dasgupta, Papadimitriou, & Vazirani in their Algorithms, 2006) call the Hamilton path the "Rudrata path" after the Kashmiri poet Rudrata who originated the concept of the knight's tour on a chessboard. I don't think this term is widespread enough yet to be worth including in the article, but it may be worth thinking about in future. Gdr 11:57, 10 April 2007 (UTC)
thread_title:  Rudrata path 

message: *I think we might need a better example image - at first I just stared at the image unsure what to look for. After refreshing my memory I noticed that the black line was actually the path travelled. I slighly updated the description, but I think we need a better example here. CharonX/talk 19:32, 14 April 2007 (UTC)
replies: text: I added an example I found on  the German Wikipedia article. Maybe the other one should be removed, it seems somewhat hard to follow. Arthena(talk) 21:45, 26 October 2007 (UTC)
thread_title:  Better example image 

message: Why does this article seem to contradict itself?
"every [[tournament] has an odd number of Hamiltonian paths"
"A tournament (with more than 2 vertices) is Hamiltonian if and only if it is strongly connected."
These statements do not seem to agree. --AlanH (talk) 18:40, 22 February 2008 (UTC)
thread_title:  Contradiction: Tournaments 

message: "every platonic solid, considered as a graph, is Hamiltonian".  Since there are only 5 platonic solids this is rather uninteresting.  Does the result generalize to regular polytopes?  85.166.68.45 (talk) 11:50, 22 July 2009 (UTC)
thread_title:  platonic solids 

message: Does this game fall within this article's scope? If not, is it worth a separate article?  —Preceding unsigned comment added by 72.72.49.169 (talk) 16:33, 8 November 2009 (UTC)
thread_title: Numbrix game 

message: "vertex has a full degree smaller than n." could someone can explain what does "full degree" means?  --Arthur MILCHIOR (talk) 01:09, 7 January 2010 (UTC)
thread_title:  Full degree 

message: *Confusion making As evidenced by AlanH's  comment in the section Contradiction: tournaments, the use of the term "Hamiltonian Graph" is misleading and confusing. Because this page introduces two distinct but similar ideas, the Hamiltonian path and the Hamiltonian circuit, readers who read only part of the definitions section will be confused, and may leave with misinformation if they assume that "Hamiltonian graph" means a graph that contains a Hamiltonian path. This assumption is perfectly logical given that the term is introduced on an article titled Hamiltonian path.  I recommend either we discuss Paths and Circuits on separate pages, or remove the definition "Hamiltonian graph" and ensure that all theorems state instead, that a graph "contains a Hamiltonian circuit". Clifsportland (talk) 01:16, 17 May 2010 (UTC)
replies: text: I'm sure its definition could be clarified, but the term "Hamiltonian graph" is a very common term, and should be defined here. "Hamiltonian circuit" and "Hamiltonian path" have too much in common to each have their own articles.  I think we should simply work to clarify the confusing parts of the existing article. Justin W Smith talk/stalk 01:35, 17 May 2010 (UTC)
replies: text:  Should we replace "Hamiltonian" in the theorems with "contains a Hamiltonian circuit"? This would clarify the article quite a bit, while leaving "Hamiltonian" defined for those who wish to use it or discover its meaning. Clifsportland (talk) 07:17, 18 May 2010 (UTC)
thread_title:  Remove term "Hamiltonian Graph" 

message: I'm not sure these belong on this page. Whether they perform properly is one question, Whether they are original research is yet another. Also, since the algorithms in question came from other forums there is a question of copyright. I suggest removing them to this talk page. Cliff (talk) 17:54, 20 March 2011 (UTC)
replies: text: This can be safely removed, and not only for the reasons you state. Algorithms that solve “a subset” of the instances, in particular if that subset is ill defined, are not noteworthy. Thore Husfeldt (talk) 19:37, 20 March 2011 (UTC)
thread_title:  Computer Programming algorithms.  

message: There are "citation needed" tags on the claims that all prism and antiprism graphs are Hamiltonian. Is that really necessary? These claims seem easily verified by the reader.
myncknm (talk) 21:17, 6 September 2012 (UTC)
replies: text: If that's so easy, why not add the demonstration or a source? --MathsPoetry (talk) 13:41, 3 January 2013 (UTC)
thread_title:  Prism graphs are Hamilitonian 

message: In case anyone's interested, I have added a number of new images to illustrate this article on the French Wikipedia. Best, --MathsPoetry (talk) 13:17, 3 January 2013 (UTC)
thread_title:  New images 

message: the definition of "closure" given in the section on the Bondy-Chvatal theorem obviously isn't the right one. Obviously, because you cannot create a situation where the degree inequality fails to hold by adding edges (nor does this procedure have any effect if you start with a graph with a small number of edges). Most likely the sense of the inequality is backwards. Someone who knows a reference on this should fix it.
123.234.83.138 (talk) 23:37, 7 June 2014 (UTC)
replies: text: No, I think it's correct. The point is that by adding edges between pairs of vertices for which the degree inequality is already true, you can make the inequality true for other pairs as well. And it shouldn't have an effect on sparse graphs, because many of those are non-Hamiltonian and it would be incorrect for this procedure to turn a non-Hamiltonian graph into a Hamiltonian one. —David Eppstein (talk) 23:49, 7 June 2014 (UTC)
thread_title:  incorrect definition of closure 

message: The topic of a Hamiltonian decomposition (partition of edges into Hamiltonian circuits) is broached in the article, but nothing of substance is said about e.g. conditions for existence of such.  Possibly this deserves its own article; an early (19th century) result in graph theory is the theorem of Walecki shows a complete graph on an odd number of vertices has a Hamiltonian decomposition.  At a glance no mention of this appears in any Wikipedia article, yet.
I think a start would be to expand the current article with a section on that topic.
Hardmath (talk) 16:54, 25 September 2017 (UTC)
thread_title:  Hamiltonian decomposition 

message: An Eulerian path is one that visits every edge, whereas a Hamiltonian path is one that visits every vertex. Do you think the expected reader might accidentally confuse the two?
Just wanted to ask cos I wasn't certain.
EditorPerson53 (talk) 22:12, 15 May 2022 (UTC)
thread_title:  Should we add "Not to be confused with Eulerian path"?