Talk:Graph minor

message: Note: "branch sets" are used, but are never defined nor linked to.  
71.139.164.223 (talk) 18:30, 21 December 2011 (UTC)
replies: text: I agree. Can anybody fix the example (or the definition) please? Now I see; the example actually works, as edge deletions are included in the definition of subgraph. The explanation of the example is confusing, though. IMHO, the contractions should be done on the subgraph of G obtained by deleting the "oblique" edges, and so it would be better to use a new image too. fudo (questions?) 13:28, 26 April 2007 (UTC)
replies: text:  Fixed --- pom 09:51, 1 September 2006 (UTC)
thread_title: Untitled

message: *In graph theory, a graph H is called a minor of the graph G if H is isomorphic to a graph that can be obtained [...]
**Isomorphic as in Graph isomorphism? --Abdull (talk) 12:11, 28 July 2008 (UTC)
replies: text: I generally agree with all this, but I think leaving the class of connected graphs is a legitimate thing to do, for instance in the context of pseudoforests. Note that in that context there is an issue with what to do with loops, as mentioned in that article — if one only considers minors that are simple graphs, without loops and multiple adjacencies, then there are two forbidden minors with four and five vertices, while if loops are allowed then the forbidden minor characterization is much simpler, the single forbidden minor being a vertex with two loops. Your comments above don't mention edge multiplicity, though — how do you prefer that to be handled? Anyway, it would perhaps be easiest if you just went ahead and made these changes; if others quibble they can modify your edits. —David Eppstein (talk) 23:24, 21 January 2009 (UTC)
thread_title:  Isomorphic 

message: Substituted at 18:20, 17 July 2016 (UTC)
thread_title: Assessment comment

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thread_title:  External links modified 

message: At present the definition in the article states:
: An undirected graph H is a minor of another undirected graph G if a graph isomorphic to H can be obtained from G by contracting some edges, deleting some edges, and deleting some isolated vertices. (emphasis mine)
Is there some reason this cannot be simplified to the following?
: An undirected graph H is a minor of another undirected graph G if a graph isomorphic to H can be obtained from G by contracting some edges and deleting some edges and vertices.
This definition can be obtained easily from the first as you can isolate any vertex you want by deleting all the edges leading to it, and then delete the isolated vertex. So the former definition seems unnecessarily complicated. --Saforrest (talk) 10:10, 19 October 2020 (UTC)
thread_title:  Unnecessarily complicated definition? 

message: RFC on the topic of graph majors, which are graphs that contain G as a minor, and can be constructed from G by INSERTing edges and vertices, and EXPANDing edges.
Darcourse (talk) 06:00, 16 December 2021 (UTC)
thread_title:  Graph major 

message: Butterfly minors and strong minors are fairly major types. They are discussed in many publications, but don't appear in the list of common variations. A recent paper discussing how they could be applied to digraphs is here, and has the virtue of containing many references to classic undirected theory.  (also available on arxiv). Someone with more experience than me will need to discuss strong minors, but butterfly minors are created by either 1) deleting an edge, or 2) contracting an edge (a,b) if it is either the only only outgoing edge of a or the only incoming edge of b Oceanchaos (talk) 05:25, 11 August 2022 (UTC)
thread_title:  More Entries under Variations