Chromatic polynomial M
- (V
, E )
f : V -
s
eyed
ti Efx] VE EE
Eff
- '
Ci)
- Pye
Claim :
IT
'
Rb
www.alctf-XCX
- D
- - (x -KH)
1 IT partition
deg = n
k classes
monic
- Claim : Pye www.alctf-XCX IT Rb ' - - ( x - KH ) - D 1 IT - - PDF document
Chromatic polynomial - ( V , E ) M - eyed f : V - s ti Efx ] VE EE - ' Eff Ci ) - Claim : Pye www.alctf-XCX IT Rb ' - - ( x - KH ) - D 1 IT partition deg = n k classes monic E legal HE 172 illegal Pfe '= pgelxi-pE.cn HE Hi
Chromatic polynomial M
, E )
f : V -
s
eyed
ti Efx] VE EE
Eff
Ci)
Claim :
IT
'
Rb
www.alctf-XCX
1 IT partition
deg = n
k classes
monic
HE 172
E legal
illegal
Pfe'¥= pgelxi-pE.cn
← → HE
.
6,6)
contraction
)=×n
remove t FEE
c-* for regular
r-uniform
c-* = en
hypergraph
r
cover:
Yi
'Tr
Ey,
=I
Z
c-*
Exe
't tdedeg
t
*
z v * IF IT
*
c-Ema
DIDNOT
r
USE
LPIR
prog planes
2
, T
✓ =L
Xo
a line
is
a cover -
(1)
ISI = n
covers
⇐ I
edges 44 2N T
er . u deg
Intl) .I
(3) T Z t *
= wtf
" = ht ¥
, 7h
Claim
T Intl
(2)
T
cover
ITI *
I Pl
x -4T
lines
U
v*=T*=ht¥
,
E-htt
V Ld
c- = T
en
possibly def
prog
' plane⇒ IPKILI
A ,
. . . AmEcn)
I Ain Ajtf
ti Fj
(Ail
> f
m E n
thiel 22
Z
Xo
dual
H
← us
'II's
I.
'it
.
c-* E 2 - I, e
" '÷
#
n.aitg
I
=h - rt l
'
C- ' = h - r
TAM VIE
is
AB
'
,
. " . Emmy met# cover¥:
.
Hadamard 's Inez
A - Ca.
. . . an)Idet
,Al EII Hai"
vol
equal if
arts
.Gran -Schmidt orblog
.# mex
Ebentown families
HT > 2K
convfpem)
A -
. . an)
WLOG
NTS
lditAl - 1
AtA
= (I
' -7) FanidefXi ZO
E Xi
= trace = n
IT Xi
= dit LATA)=
det LAT)
.det CA)NTS
= det (A)2
ITX