id: 06053934
dt: j
an: 06053934
au: Li, Bo-Jr; Chang, Gerard J.
ti: The competition number of a graph with exactly two holes.
so: J. Comb. Optim. 23, No. 1, 1-8 (2012).
py: 2012
pu: Springer, Dordrecht
la: EN
cc: 
ut: competition graph; competition number; chordal graph; chordless cycle; hole
ci: 
li: doi:10.1007/s10878-010-9331-9
ab: Summary: Given an acyclic digraph $D$, the competition graph $C(D)$ of $D$
    is the graph with the same vertex set as $D$ and two distinct vertices
    $x$ and $y$ are adjacent in $C(D)$ if and only if there is a vertex $v$
    in $D$ such that $(x,v)$ and $(y,v)$ are arcs of $D$. The competition
    number $κ(G)$ of a graph $G$ is the least number of isolated vertices
    that must be added to $G$ to form a competition graph. The purpose of
    this paper is to prove that the competition number of a graph with
    exactly two holes is at most three.
rv: