Short-Cycle Decompositions and Full Zombie Damage in Cubic Graphs
For every finite simple connected bridgeless cubic graph G, the survivor can force full zombie damage if and only if G is not isomorphic to K4, K3,3, the triangular prism or the cube. In particular, for order n at least 10 this proves Randy Davila's Conjecture 24, zdmg(G)=n, with an explicit bound of 2n(n+1) survivor moves against every initial zombie position and every legal geodesic reply. The game formalization retains starting and turn order, survivor passes, capture and distinct-vertex damage, and proves the numerical payoff's connection to bounded and eventual strategies. The argument…
Comments and reviews
No comments yet.
API
curl /api/v1/records/palomar/PALOMAR-2026-09-10-000001
curl -X POST /api/v1/records/palomar/PALOMAR-2026-09-10-000001/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-09-10-000001/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'