Clique Cover Width and Clique Sum

Abstract

For a clique cover $C$ in the undirected graph $G$, the clique cover graph of $C$ is the graph obtained by contracting the vertices of each clique in $C$ into a single vertex. The clique cover width of G, denoted by $CCW(G)$, is the minimum value of the bandwidth of all clique cover graphs of $G$. When $G$ is the clique sum of $G_1$ and $G_2$, we prove that $CCW(G)\le 3/2(CCW(G_1)+CCW(G_2))$.

References in corpus (2)

• New representation results for planar graphs
• A new separation theorem with geometric applications