Question

Suppose you are organizing a dinner party. The guests are going to be seated around a single roundtable. Show that if each guest knows at least half of the other guests, then everyone can be seated next to two people they know.

Answer 1

Given ach guest knows atleast half of the othes quests le-t -a.γ χ guests αγ e Invited ' Con sıdex χ/2 g ues ts as one 9ou p and othe guests as he quand tae that each guest in one ger every guest in other group Nou asange them as attesn ative OUP Knous ves t from group that is one upone and ee3 oom 9uest f One guest from other grDup othe DUP .

then evenone tw ould Knous t People Seated nextto th em erample 'tet ftsst 3 ae roup one and nent 3 guests ase group to & guests ane inited tet guests from 9DUP one tnous each 93Dup One knous each gest rom goup t too and Vice vessa ① Knows 4,5,6 knows,, 6 9,6, knoos,2,3 asr an gement s altesnative guests from each oup ie 3