bandwidth + (treewidth - pathwidth) = treebandwidth

[N-Coder]

I wanted to point you to this paper here:
https://arxiv.org/pdf/2502.11674v1
There's multiple things in there that could be interesting:

• They have a parameter relationship diagram in Figure 8 on page 36, where they relate multiple parameters which seem to be missing from HOPS (domino treewidth, (slim) tree-cut width, edge-treewidth, tree-partition-width, fan number, dipole number,...).
• They give a list of parametric obstructions for a lot of parameters in Table 1 of page 38, maybe such overview would also be useful for HOPS.
• They relate multiple well-known parameters to maximum clique number in completions into certain graph classes (Figure 1 on page 5) as well as various graph search strategies (Figure 2 on page 6).
• They introduce the parameter treebandwidth, which nicely fills a gap in the two diagrams mentioned above.

[vaclavblazej]

Thanks for the link. I heard about treebandwidth last week for the first time. The pointed-out overview is also nice, I'll put these things in and hopefully deploy in around a month -- there are some other things I'd like to have there by then as well.

[vaclavblazej]

I've transcribed the mentioned Hasse diagram into my local hierarchy, but for each of the added parameters one should add at least some source and some definition. As this issue mentions many things that I'd like to sort out gradually, I created several bite-sized sub-issues. I'm currently working on different features but will add the parameters eventually; the parametric obstructions and graph search strategies will have to wait a little while.