C (gcc), 790 778 757 748 731 687 642 638632 bytes
typedef struct F F;typedef struct{int c,p;F**m;}g;struct F{int d;g f;};g*a,S,y,q,*x=&y,*p=&q,Q;A(g*g,F*s){g->c++[g->m=g->c-g->p?g->m:realloc(g->m,(g->p+=32)*20)]=s;}i,c[999],b,j,k,l,*s;*B(d){s=0;for(i=S.c;i--;)s=S.m[i]->d-d?s:S.m[i];!s?s=calloc(5,4),*s=d,A(&S,s):0;return s;0;s=s;}F*u,*v;E(){for(i=-1;b=++i<S.c;b&&A(x,S.m[i]))for(l=x->c;k=l--&&b;b&=*b;b&=!k)for(j=(Q=x->m[l]->f).c;j--&&(k=Q.m[j]->d-S.m[i]->d););x->c>p->c?a=x,x=p,p=a:0;x->c=0;}main(){for(;~scanf("%d %d",&a,&b)&&A(&(u=B(a))->f,v=B(b))|~A(&v->f,u););for(E();b<S.c;)c[b]>=b?c[b++]=0:E(S.m[b]=a,S.m[i]=S.m[b],a=S.m[i=b%2*c[b]++]);for(printf("%d,",i=p->c);i--;)printf(" %d",p->m[i]->d);}
This is a slightly golfed version of the reference implementation. Thanks to @jdt for -5. Try it online!Try it online!
typedef struct F F;
// student group
typedef struct{
int c, // count
p; // capacity
F**m; // members
}g;
// student
struct F{
int d; // id
g f; // friends
};
g*a,S,y,q,*x=&y,*p=&q,Q;
A(g*g,F*s){
g->c++[g->m=g->c-g->p?g->m:realloc(g->m,(g->p+=32)*20)]=s;
}
i,c[999],b,j,k,l,*s;
*B(d){
s=0;
for(i=S.c;i--;)
s=S.m[i]->d-d?s:S.m[i];
!s?
s=calloc(5,4),
*s=d,
A(&S,s)
:
0;
return s;s=s;
}
F*u,*v;
E(){
for(i=-1;b=++i<S.c;b&&A(x,S.m[i]))
for(l=x->c;k=l--&&b;b&=*b;b&=!k)
for(j=(Q=x->m[l]->f).c;j--&&(k=Q.m[j]->d-S.m[i]->d););
x->c>p->c?
a=x,
x=p,
p=a
:
0;
x->c=0;
}
main(){
for(;~scanf("%d %d",&a,&b)&&A(&(u=B(a))->f,v=B(b))|~A(&v->f,u););
for(E();b<S.c;)
c[b]>=b?
c[b++]=0
:
E(S.m[b]=a,S.m[i]=S.m[b],a=S.m[i=b%2*c[b]++]);
for(printf("%d,",i=p->c);i--;)
printf(" %d",p->m[i]->d);
}