Clique Cover Width and Clique Sum

Farhad Shahrokhi

arXiv:1502.06165·math.CO·February 26, 2015·1 cites

Clique Cover Width and Clique Sum

Farhad Shahrokhi

PDF

Open Access

TL;DR

This paper introduces the concept of clique cover width in graphs and establishes an upper bound on the clique cover width of a graph formed by the clique sum of two graphs, relating it to their individual clique cover widths.

Contribution

It provides a new bound on the clique cover width for graphs formed by clique sums, advancing understanding of graph bandwidth properties.

Findings

01

Established an upper bound: CCW(G) ≤ 1.5 (CCW(G1) + CCW(G2)) for clique sums.

02

Connected clique cover width to graph decomposition methods.

03

Enhanced theoretical understanding of graph bandwidth in composite graphs.

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 $C C W (G)$ , 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 $C C W (G) \leq 3/2 (C C W (G_{1}) + C C W (G_{2}))$ .

Peer Reviews

No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.

Videos

No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.

Taxonomy

TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Limits and Structures in Graph Theory