I believe correctness about clique in even-hole-free graphs
of [graphclasses.org](http://graphclasses.org/classes/gc_547.html)
and the paper [Vertex elimination orderings for hereditary graph classes, Pierre Aboulker, Pierre Charbit, Nicolas Trotignon, Kristina Vuskovic](http://arxiv.org/abs/1205.2535) would imply $P=NP$.


Accordinth to graphclasses: 


Clique: NP-complete by IS on complement, 


the comeplement
is related to [IS on 2-subdivision](http://graphclasses.org/classes/gc_472.html)
citing S. Poljak, A note on the stable sets and coloring of graphs
Comment. Math. Univ. Carolin. 15 (1974) 307-309 ZMath 0284.05105


According to the paper, p. 4:


(Improve) Maximum weighted clique in even-hole-free graphs in time $O(nm)$.


Related paper is [LexBFS, structure and algorithms, Pierre Aboulker, Pierre Charbit, Maria Chudnovsky, Nicolas Trotignon, Kristina Vuskovic](http://xxx.tau.ac.il/abs/1205.2535v1) which claims the same.


The sources appear credible to me, though an error is
certainly possible.


*Added* [Third paper](http://www.sciencedirect.com/science/article/pii/S0012365X06006248/pdfft?md5=d101ec815e12cc3075eb6be33b9f25ca&pid=1-s2.0-S0012365X06006248-main.pdf) gives $O(n^2m)$ algorithm for MWC.


On graph classes, to get an explanation about complexity
click on [+]Details.



> 
> What went wrong?
> 
> 
> 



Seeming contradiction about P vs NP between graphclasses.org and at least two papers about clique in even-hole-free graphs
On <http://www.graphclasses.org>, an even hole means at least 6 vertices. If you open the details of the forbidden subgraphs list of the page for even-hole-free graphs and click on the link for even-hole, you'll see the definition.


In the articles you refer to, an even hole means at least 4 vertices. The even-hole-free of the articles is what on graphclasses.org is called [even-cycle-free](http://graphclasses.org/classes/gc_706.html).


Hence, P=NP is still open.


