Linear clique-width lcw(G): clique-width with linear (sequential, non-branching) expression trees. lcw ≥ cw. As pathwidth is to treewidth, lcw is to cw. Captures 'linear' dense structure. lcw = pw for sparse graphs (roughly).
How to Use
Select graph:
- lcw: Linear cw
- vs cw: Compare
- Linear: No branching
Linear vs General
Clique-width: expression tree can branch (disjoint union). Linear: each step adds one vertex (like pathwidth). lcw ≥ cw since we lose the branching power. Gap can be exponential in theory.
NLC-Width
Closely related to NLC-width (node label controlled). Same expressiveness as clique-width up to exponential factor. Linear NLC-width = linear clique-width (essentially). Different names, same concept.
Step-by-Step Instructions
- 1Select graph.
- 2Build linear expr.
- 3Count labels.
- 4Compare with cw.
- 5Check gap.