{"id":"palomar/PALOMAR-2026-09-10-000001","url":"https://github.com/lennrt/palomar-formalizations/tree/f8f870fb1ce96d966ff39a8470f7f57011c398bb/zenodo-22667596/palomar","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-10-000001-v1.json","repo":"https://github.com/lennrt/palomar-formalizations","tags":["math.CO","cs.LO","msc:05C57","msc:05C75","msc:68V20","graph-theory","combinatorial-games","zombie-game","cubic-graphs"],"score":0,"title":"Short-Cycle Decompositions and Full Zombie Damage in Cubic Graphs","trust":"high","domain":"math.CO","source":"palomar","authors":["Lennart Rudolph"],"reviews":0,"subject":"math.CO","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-10","reactions":{},"formalized":true,"formalizes":[{"title":"Short-Cycle Decompositions and Full Zombie Damage in Cubic Graphs","identifier":"doi:10.5281/zenodo.22667596","relationship":"formalizes"},{"title":"The Zombie Damage Number of a Graph","identifier":"arxiv:2607.16382v1","relationship":"formalizes"}]}