From sterten at posteo.de  Sat Feb 14 16:59:05 2026
From: sterten at posteo.de (sterten at posteo.de)
Date: Sat, 14 Feb 2026 05:59:05 +0000
Subject: [Nauty] Hamiltonian Cycle gadgets
Message-ID: <326876e491bfd595b4a3a5d5a8b30a8e@posteo.de>

hello graph-people ,

given a (very) small undirected,simple graph G, I want to find a larger
simple,undirected graph H containing G's vertices such that

(1) there is a Hamiltonian Path v<->w in H , iff there is an edge (v,w) 
in G
and
(2) H cannot be partitioned into 2 or more disjoint paths starting and 
ending
at vertices from G.

here is a picture of what I have so far :
http://magictour.free.fr/gadgetn.GIF

what's an efficient method to search systematically ?
Maybe searching/pruning all suitable Hs and listing the Gs which they
extend ?


Guenter Stertenbrink

https://knighttours.createaforum.com/general-hamiltonian-cycles-problem/
http://magictour.free.fr