From d1a4616ac423e9b8755b39e05e9713333bc54a49 Mon Sep 17 00:00:00 2001
From: giles <giles.bradshaw@rose-ash.com>
Date: Sun, 10 May 2026 23:08:16 +0000
Subject: [PATCH] ocaml: phase 5.1 bipartite.ml baseline (7-node bipartite, 4
 in color 0)

BFS-based 2-coloring of an undirected graph:

  edges (undirected):
    0-1  0-3  1-2  1-4  2-5  3-4  3-6  5-6

  Partition: {0, 2, 4, 6} vs {1, 3, 5} (no odd cycles)

Returns count of color-0 vertices (4) on success, -1 on odd-cycle
detection.

Tests Queue-based BFS with a source-loop wrapper for disconnected
graphs, `1 - color.(u)` toggle, color-equality conflict check
on already-colored neighbors.

164 baseline programs total.
---
 lib/ocaml/baseline/bipartite.ml  | 39 ++++++++++++++++++++++++++++++++
 lib/ocaml/baseline/expected.json |  1 +
 plans/ocaml-on-sx.md             |  9 ++++++++
 3 files changed, 49 insertions(+)
 create mode 100644 lib/ocaml/baseline/bipartite.ml

diff --git a/lib/ocaml/baseline/bipartite.ml b/lib/ocaml/baseline/bipartite.ml
new file mode 100644
index 00000000..cb027281
--- /dev/null
+++ b/lib/ocaml/baseline/bipartite.ml
@@ -0,0 +1,39 @@
+let is_bipartite n adj =
+  let color = Array.make n (-1) in
+  let ok = ref true in
+  let q = Queue.create () in
+  for src = 0 to n - 1 do
+    if color.(src) = -1 then begin
+      color.(src) <- 0;
+      Queue.push src q;
+      while not (Queue.is_empty q) do
+        let u = Queue.pop q in
+        List.iter (fun v ->
+          if color.(v) = -1 then begin
+            color.(v) <- 1 - color.(u);
+            Queue.push v q
+          end else if color.(v) = color.(u) then
+            ok := false
+        ) adj.(u)
+      done
+    end
+  done;
+  let zeros = ref 0 in
+  for i = 0 to n - 1 do
+    if color.(i) = 0 then zeros := !zeros + 1
+  done;
+  if !ok then !zeros else -1
+
+;;
+
+let n = 7 in
+let adj = [|
+  [1; 3];
+  [0; 2; 4];
+  [1; 5];
+  [0; 4; 6];
+  [1; 3];
+  [2; 6];
+  [3; 5]
+|] in
+is_bipartite n adj
diff --git a/lib/ocaml/baseline/expected.json b/lib/ocaml/baseline/expected.json
index 84cee1ff..7e246220 100644
--- a/lib/ocaml/baseline/expected.json
+++ b/lib/ocaml/baseline/expected.json
@@ -12,6 +12,7 @@
   "bisect.ml": 141,
   "bigint_add.ml": 28,
   "binary_heap.ml": 123456789,
+  "bipartite.ml": 4,
   "bits.ml": 21,
   "balance.ml": 3,
   "base_n.ml": 17,
diff --git a/plans/ocaml-on-sx.md b/plans/ocaml-on-sx.md
index c49c7565..e79e89ab 100644
--- a/plans/ocaml-on-sx.md
+++ b/plans/ocaml-on-sx.md
@@ -407,6 +407,15 @@ _Newest first._
   binary search tree (`type 'a tree = Leaf | Node of 'a * 'a tree *
   'a tree`) with insert + in-order traversal. Tests parametric ADT,
   recursive match, List.append, List.fold_left.
+- 2026-05-10 Phase 5.1 — bipartite.ml baseline (BFS 2-coloring on
+  7-node cycle-rich graph → bipartite with 4 vertices in color 0).
+  Edges: 0-1, 0-3, 1-2, 1-4, 2-5, 3-4, 3-6, 5-6. This forms a
+  bipartite graph with partition {0,2,4,6} vs {1,3,5}. Returns
+  count of color-0 vertices (4) on success, -1 on odd-cycle
+  detection. Tests Queue-based BFS with module-level state in a
+  loop over all sources (handles disconnected graphs), `1 - color.(u)`
+  binary toggle, color-equality conflict check. 164 baseline
+  programs total.
 - 2026-05-10 Phase 5.1 — egg_drop.ml baseline (worst-case trials
   for 2 eggs, 36 floors = 8). Classic O(e·f²) DP: dp[e][f] = 1 +
   min over k of max(dp[e-1][k-1], dp[e][f-k]). Closed form via