Fix #47: Add HamiltonianCycle model (#57)

* Add plan for #47: [Model] HamiltonianCycle

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

* feat: add HamiltonianCycle model (#47)

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

* docs: add HamiltonianCycle definition to paper (#47)

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

* refactor: rename HamiltonianCycle to TravelingSalesman (#47)

Resolve PR review comments: weighted HamiltonianCycle is equivalent to
the Traveling Salesman Problem, so rename accordingly. Also fix problem
definition to properly define the edge set C.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

---------

Co-authored-by: Claude Opus 4.6 <noreply@anthropic.com>

Author: GiggleLiu

docs/paper/reductions.typ

@@ -31,6 +31,7 @@
   "KColoring": [$k$-Coloring],
   "MinimumDominatingSet": [Minimum Dominating Set],
   "MaximumMatching": [Maximum Matching],
+  "TravelingSalesman": [Traveling Salesman],
   "MaximumClique": [Maximum Clique],
   "MaximumSetPacking": [Maximum Set Packing],
   "MinimumSetCovering": [Minimum Set Covering],
@@ -324,6 +325,10 @@ In all graph problems below, $G = (V, E)$ denotes an undirected graph with $|V|
   Given $G = (V, E)$ with weights $w: E -> RR$, find $M subset.eq E$ maximizing $sum_(e in M) w(e)$ s.t. $forall e_1, e_2 in M: e_1 inter e_2 = emptyset$.
 ]
 
+#problem-def("TravelingSalesman")[
+  Given an undirected graph $G=(V,E)$ with edge weights $w: E -> RR$, find an edge set $C subset.eq E$ that forms a cycle visiting every vertex exactly once and minimizes $sum_(e in C) w(e)$.
+]
+
 #problem-def("MaximumClique")[
   Given $G = (V, E)$, find $K subset.eq V$ maximizing $|K|$ such that all pairs in $K$ are adjacent: $forall u, v in K: (u, v) in E$. Equivalent to MIS on the complement graph $overline(G)$.
 ]