Question

8.15 points]A triangle in an undirected graph is a 3-clique. Show that TRIANGLE E P, where TRIANGLE= <G>| G contains a triangle}

Answer 1

Solutop languagesthat are doteminite class p P is a class ap a On Polynomial tme de cidable im Sinle tape ti ing machine. Given tcangle undirected is an 9Taph is a 3-cligue hiang'e TRIANGLE = (G >IGcontains TRIANGLE EP shouw the To -> Let A be he Turin machine thaf decedes TRIANGLE is polynomial me Now A Can be described as input Gv, ES Set op verkces 0.f the Here graph G E set of Edges af the 9raph G cs Scanned with CamScanner

and uv zw enumerate all tples <u,v edges Cu, lv, ) and (w,u) exict im E or not. DP Exist- then 2. Check hhether all Aree aсcept 3 otherusise rejeck . Tple reguire >Enumesateon op alt >checking whether all he ree edges belon take (IEI) Eme to E Lohich is polynomial Overall me f o(v(El) inplet in 4he lenyth of the TRIANGLE EP CS Scanned with CamScanner