For every fixed graphH, we determine theH-covering number ofKn, for alln>n0(H). We prove that ifhis the number of edges ofH, andgcd(H)=dis the greatest common divisor of the degrees ofH, then there existsn0=n0(H), such that for alln>n0,C(H,Kn)=dn2hn-1d,unlessdis even,n=1 moddandn(n-1)/d+1=0 mod(2h/d), in which case[formula]Our main tool in proving this result is the deep decomposition result of Gustavsson.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics