Rename IsHamiltonianPath to IsHamiltonianCycle

Author: wilfwilson

doc/attr.xml

@@ -1579,43 +1579,44 @@ gap> FacialWalks(D3, rot);
 </ManSection>
 <#/GAPDoc>
 
-<#GAPDoc Label="HamiltonianPath">
+<#GAPDoc Label="HamiltonianCycle">
 <ManSection>
-  <Attr Name="HamiltonianPath" Arg="digraph"/>
+  <Attr Name="HamiltonianCycle" Arg="digraph"/>
   <Returns>A list or <K>fail</K>.</Returns>
   <Description>
-    Returns a Hamiltonian path if one exists, <K>fail</K> if not.<P/>
+    For a digraph <A>digraph</A>, this attribute returns a Hamiltonian cycle,
+    if one exists, and <K>fail</K> if one does not.<P/>
 
-    A <E>Hamiltonian path</E> of a digraph with <C>n</C> vertices is directed
+    A <E>Hamiltonian cycle</E> of a digraph with <C>n</C> vertices is a directed
     cycle of length <C>n</C>. If <A>digraph</A> is a digraph that contains a
-    Hamiltonian path, then this function returns one, described in the form
-    used by <Ref Attr="DigraphAllSimpleCircuits"/>. Note if <A>digraph</A> has
-    0 or 1 vertices, then <C>HamiltonianPath</C> returns <C>[]</C> or
+    Hamiltonian cycle, then this function returns one, described in the form
+    used by <Ref Attr="DigraphAllSimpleCircuits"/>. Note that if <A>digraph</A>
+    has 0 or 1 vertices, then <Ref Attr="HamiltonianCycle"/> returns <C>[]</C> or
     <C>[1]</C>, respectively.<P/>
 
     The method used in this attribute has the same worst case complexity as
     <Ref Oper="DigraphMonomorphism"/>.
 
     <Example><![CDATA[
-gap> D := Digraph([[]]);
+gap> D := EmptyDigraph(1);
 <immutable empty digraph with 1 vertex>
-gap> HamiltonianPath(D);
+gap> HamiltonianCycle(D);
 [ 1 ]
-gap> D := Digraph([[2], [1]]);
-<immutable digraph with 2 vertices, 2 edges>
-gap> HamiltonianPath(D);
+gap> D := CycleDigraph(2);
+<immutable cycle digraph with 2 vertices>
+gap> HamiltonianCycle(D);
 [ 1, 2 ]
 gap> D := Digraph([[3], [], [2]]);
 <immutable digraph with 3 vertices, 2 edges>
-gap> HamiltonianPath(D);
+gap> HamiltonianCycle(D);
 fail
-gap> D := Digraph([[2], [3], [1]]);
-<immutable digraph with 3 vertices, 3 edges>
-gap> HamiltonianPath(D);
+gap> D := CycleDigraph(3);
+<immutable cycle digraph with 3 vertices>
+gap> HamiltonianCycle(D);
 [ 1, 2, 3 ]
 gap> D := GeneralisedPetersenGraph(IsMutableDigraph, 5, 2);
 <mutable digraph with 10 vertices, 30 edges>
-gap> HamiltonianPath(D);
+gap> HamiltonianCycle(D);
 fail
 ]]></Example>
   </Description>

doc/examples.xml

@@ -1064,7 +1064,7 @@ gap> D := CirculantGraph(6, [2, 3]);
  with 6 vertices, 18 edges>
 gap> AutomorphismGroup(D) = DihedralGroup(IsPermGroup, 12);
 true
-gap> HamiltonianPath(D);
+gap> HamiltonianCycle(D);
 [ 1, 3, 5, 2, 6, 4 ]
 gap> IsCompleteDigraph(CirculantGraph(6, [1, 2, 3]));
 true]]></Example>

doc/prop.xml

@@ -956,21 +956,21 @@ true
     &MUTABLE_RECOMPUTED_PROP;
 
     <Example><![CDATA[
-gap> g := Digraph([[]]);
+gap> D := EmptyDigraph(1);
 <immutable empty digraph with 1 vertex>
-gap> IsHamiltonianDigraph(g);
+gap> IsHamiltonianDigraph(D);
 true
-gap> g := Digraph([[2], [1]]);
-<immutable digraph with 2 vertices, 2 edges>
-gap> IsHamiltonianDigraph(g);
+gap> D := CycleDigraph(2);
+<immutable cycle digraph with 2 vertices>
+gap> IsHamiltonianDigraph(D);
 true
-gap> g := Digraph([[3], [], [2]]);
+gap> D := Digraph([[3], [], [2]]);
 <immutable digraph with 3 vertices, 2 edges>
-gap> IsHamiltonianDigraph(g);
+gap> IsHamiltonianDigraph(D);
 false
-gap> g := Digraph([[2], [3], [1]]);
-<immutable digraph with 3 vertices, 3 edges>
-gap> IsHamiltonianDigraph(g);
+gap> D := CycleDigraph(3);
+<immutable cycle digraph with 3 vertices>
+gap> IsHamiltonianDigraph(D);
 true
 ]]></Example>
   </Description>

doc/z-chap4.xml

@@ -85,7 +85,7 @@
     <#Include Label="DigraphLayers">
     <#Include Label="DigraphDegeneracy">
     <#Include Label="DigraphDegeneracyOrdering">
-    <#Include Label="HamiltonianPath">
+    <#Include Label="HamiltonianCycle">
     <#Include Label="NrSpanningTrees">
     <#Include Label="DigraphDijkstra">
     <#Include Label="DigraphCycleBasis">

gap/attr.gd

@@ -66,7 +66,7 @@ DeclareOperation("DigraphAllChordlessCyclesOfMaximalLength",
     [IsDigraph, IsInt]);
 DeclareAttribute("DigraphAllChordlessCycles", IsDigraph);
 DeclareOperation("FacialWalks", [IsDigraph, IsList]);
-DeclareAttribute("HamiltonianPath", IsDigraph);
+DeclareAttribute("HamiltonianCycle", IsDigraph);
 DeclareAttribute("DigraphPeriod", IsDigraph);
 DeclareAttribute("DigraphLoops", IsDigraph);
 

gap/attr.gi

@@ -2267,7 +2267,7 @@ function(D)
   return Determinant(mat);
 end);
 
-InstallMethod(HamiltonianPath, "for a digraph", [IsDigraph],
+InstallMethod(HamiltonianCycle, "for a digraph", [IsDigraph],
 function(D)
   local path, iter, n;
 

gap/prop.gi

@@ -605,11 +605,12 @@ function(D)
       return true;
     fi;
   fi;
-  return HamiltonianPath(D) <> fail;
+  return HamiltonianCycle(D) <> fail;
 end);
 
-InstallMethod(IsHamiltonianDigraph, "for a digraph with hamiltonian path",
-[IsDigraph and HasHamiltonianPath], x -> HamiltonianPath(x) <> fail);
+InstallMethod(IsHamiltonianDigraph,
+"for a digraph with known hamiltonian cycle",
+[IsDigraph and HasHamiltonianCycle], x -> HamiltonianCycle(x) <> fail);
 
 InstallMethod(IsDigraphCore, "for a digraph",
 [IsDigraph],

tst/extreme/attr.tst

@@ -41,20 +41,20 @@ gap> circs := DigraphAllSimpleCircuits(gr);;
 gap> Length(circs);
 1291792
 
-#  HamiltonianPath and IsHamiltonianDigraph
+#  HamiltonianCycle and IsHamiltonianDigraph
 gap> g := CompleteDigraph(20);
 <immutable complete digraph with 20 vertices>
-gap> HamiltonianPath(g);
+gap> HamiltonianCycle(g);
 [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 ]
 gap> IsDigraphMonomorphism(CycleDigraph(20), 
 >                          g,
->                          Transformation(HamiltonianPath(g)));
+>                          Transformation(HamiltonianCycle(g)));
 true
 gap> IsHamiltonianDigraph(g);
 true
 gap> g := CompleteMultipartiteDigraph([1, 9, 1, 1, 2, 1, 1, 1]);
 <immutable complete multipartite digraph with 17 vertices, 198 edges>
-gap> HamiltonianPath(g);
+gap> HamiltonianCycle(g);
 fail
 gap> IsHamiltonianDigraph(g);
 false

tst/standard/attr.tst

@@ -2237,110 +2237,110 @@ gap> ForAll(D,
 > d -> DigraphNrEdges(d) / 2 = DigraphNrEdges(StrongOrientation(d)));
 true
 
-#  HamiltonianPath
+#  HamiltonianCycle
 gap> g := Digraph([]);
 <immutable empty digraph with 0 vertices>
-gap> HamiltonianPath(g);
+gap> HamiltonianCycle(g);
 [  ]
 gap> g := Digraph([[]]);
 <immutable empty digraph with 1 vertex>
-gap> HamiltonianPath(g);
+gap> HamiltonianCycle(g);
 [ 1 ]
 gap> g := Digraph([[], []]);
 <immutable empty digraph with 2 vertices>
-gap> HamiltonianPath(g);
+gap> HamiltonianCycle(g);
 fail
 gap> g := Digraph([[1]]);
 <immutable digraph with 1 vertex, 1 edge>
-gap> HamiltonianPath(g);
+gap> HamiltonianCycle(g);
 [ 1 ]
 gap> g := Digraph([[2, 2], []]);
 <immutable multidigraph with 2 vertices, 2 edges>
-gap> HamiltonianPath(g);
+gap> HamiltonianCycle(g);
 fail
 gap> g := Digraph([[2], [1]]);
 <immutable digraph with 2 vertices, 2 edges>
-gap> HamiltonianPath(g);
+gap> HamiltonianCycle(g);
 [ 1, 2 ]
 gap> g := Digraph([[3], [3], []]);
 <immutable digraph with 3 vertices, 2 edges>
-gap> HamiltonianPath(g);
+gap> HamiltonianCycle(g);
 fail
 gap> g := Digraph([[3], [3], [1, 2]]);
 <immutable digraph with 3 vertices, 4 edges>
-gap> HamiltonianPath(g);
+gap> HamiltonianCycle(g);
 fail
 gap> g := Digraph([[3], [], [2]]);
 <immutable digraph with 3 vertices, 2 edges>
-gap> HamiltonianPath(g);
+gap> HamiltonianCycle(g);
 fail
 gap> g := Digraph([[2], [3], [1]]);
 <immutable digraph with 3 vertices, 3 edges>
-gap> HamiltonianPath(g);
+gap> HamiltonianCycle(g);
 [ 1, 2, 3 ]
 gap> g := Digraph([[2], [3], [1], []]);
 <immutable digraph with 4 vertices, 3 edges>
-gap> HamiltonianPath(g);
+gap> HamiltonianCycle(g);
 fail
 gap> g := Digraph([[2], [3], [1, 4], []]);
 <immutable digraph with 4 vertices, 4 edges>
-gap> HamiltonianPath(g);
+gap> HamiltonianCycle(g);
 fail
 gap> g := Digraph([[3, 6], [4], [2, 1], [5, 1], [3], [4]]);
 <immutable digraph with 6 vertices, 9 edges>
-gap> HamiltonianPath(g);
+gap> HamiltonianCycle(g);
 fail
 gap> g := Digraph([[3, 6], [4, 1], [2, 1], [5, 1], [3], [4]]);
 <immutable digraph with 6 vertices, 10 edges>
-gap> HamiltonianPath(g);
+gap> HamiltonianCycle(g);
 [ 1, 6, 4, 5, 3, 2 ]
 gap> g := Digraph([[3, 6], [4], [2, 1], [5, 1], [3], [4, 7], []]);
 <immutable digraph with 7 vertices, 10 edges>
-gap> HamiltonianPath(g);
+gap> HamiltonianCycle(g);
 fail
 gap> g := Digraph([[3, 6, 7], [4, 1], [2, 1], [5, 1], [3], [4, 7], [6]]);
 <immutable digraph with 7 vertices, 13 edges>
-gap> HamiltonianPath(g);
+gap> HamiltonianCycle(g);
 [ 1, 7, 6, 4, 5, 3, 2 ]
 gap>  g := Digraph([[3, 6], [4], [2, 1], [5, 1], [3], [4, 7], [6]]);
 <immutable digraph with 7 vertices, 11 edges>
-gap> HamiltonianPath(g);
+gap> HamiltonianCycle(g);
 fail
 gap> g := Digraph([[5, 6, 10], [2, 9], [3, 7], [2, 3], [9, 10], [2, 9], [1],
 >                  [2, 3, 4, 7, 9], [3, 10], [4, 5, 6, 8]]);
 <immutable digraph with 10 vertices, 25 edges>
-gap> HamiltonianPath(g);
+gap> HamiltonianCycle(g);
 fail
 gap> g := Digraph([[2, 4, 6, 10], [1, 3, 4, 5, 6, 7, 9, 10], [1, 5, 7, 8],
 >                  [6, 10], [1, 7], [3, 4, 6, 7, 9], [2, 3, 4, 7],
 >                  [2, 4, 5, 6], [2, 3, 5, 6, 7, 9, 10], [2, 3, 5]]);
 <immutable digraph with 10 vertices, 43 edges>
-gap> HamiltonianPath(g);
+gap> HamiltonianCycle(g);
 [ 1, 4, 6, 9, 10, 3, 8, 5, 7, 2 ]
 gap> IsDigraphMonomorphism(CycleDigraph(10),
 >                          g,
->                          Transformation(HamiltonianPath(g)));
+>                          Transformation(HamiltonianCycle(g)));
 true
 gap> g := CompleteMultipartiteDigraph([1, 30]);
 <immutable complete bipartite digraph with bicomponent sizes 1 and 30>
-gap> HamiltonianPath(g);
+gap> HamiltonianCycle(g);
 fail
 gap> g := Digraph([[2, 5, 6], [3, 1, 7], [4, 2, 8], [5, 3, 9], [1, 4, 10],
 >                  [1, 8, 9], [2, 9, 10], [3, 10, 6], [4, 6, 7], [5, 7, 8]]);
 <immutable digraph with 10 vertices, 30 edges>
-gap> HamiltonianPath(g);
+gap> HamiltonianCycle(g);
 fail
 gap> g := CompleteMultipartiteDigraph([16, 15]);
 <immutable complete bipartite digraph with bicomponent sizes 16 and 15>
-gap> HamiltonianPath(g);
+gap> HamiltonianCycle(g);
 fail
 gap> g := CompleteMultipartiteDigraph([1, 15, 1, 1, 1, 1, 1, 1]);
 <immutable complete multipartite digraph with 22 vertices, 252 edges>
-gap> HamiltonianPath(g);
+gap> HamiltonianCycle(g);
 fail
 gap> g := CycleDigraph(100);
 <immutable cycle digraph with 100 vertices>
-gap> HamiltonianPath(g);
+gap> HamiltonianCycle(g);
 [ 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 
   96, 97, 98, 99, 100, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 
   17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 
@@ -2353,7 +2353,7 @@ gap> g := DigraphAddEdges(g, [[6, 8], [8, 7], [7, 9]]);
 <immutable digraph with 513 vertices, 516 edges>
 gap> g := DigraphRemoveEdge(g, [6, 7]);
 <immutable digraph with 513 vertices, 515 edges>
-gap> HamiltonianPath(g);
+gap> HamiltonianCycle(g);
 [ 1, 2, 3, 4, 5, 6, 8, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 
   22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 
   41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 
@@ -2390,7 +2390,7 @@ gap> HamiltonianPath(g);
 gap> gr := DigraphAddEdges(DigraphAddVertex(CycleDigraph(600)),
 >                          [[600, 601], [601, 600]]);
 <immutable digraph with 601 vertices, 602 edges>
-gap> HamiltonianPath(gr);
+gap> HamiltonianCycle(gr);
 fail
 
 # DigraphCore

tst/standard/prop.tst

@@ -1636,7 +1636,7 @@ true
 gap> gr := DigraphAddEdges(DigraphAddVertex(CycleDigraph(600)),
 >                          [[600, 601], [601, 600]]);
 <immutable digraph with 601 vertices, 602 edges>
-gap> HamiltonianPath(gr);
+gap> HamiltonianCycle(gr);
 fail
 gap> IsHamiltonianDigraph(gr);
 false