Title: Searching for geodetic boundary vertices sets
1Searching for geodetic boundary vertices sets
GRACO 05
- Ignacio M Pelayo
- Departament de Matemà tica Aplicada 3
- Universitat Politècnica de Catalunya
- Barcelona, Spain
Joint work with Carmen Hernando, Mercè Mora,
Carlos Seara Jose Cáceres, M. Luz Puertas
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3contour
eccentricity
extreme set
boundary
periphery
4f
d
e
c
j
a
b
g
h
i
3
4
5
4
3
5
3
3
4
4
Ext(G)a
Per(G)a,f
Ct(G)a,c,f
Ecc(G)a,c,d,e,f,g,h
Bd(G)V-b
5zz
6zz
7abcdperiphery,contour,eccentricity,boundary
8(ecc(1), ecc(2), ecc(3), ecc(4), ecc(5),
ecc(6))(3,2,2,3,3,2)
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15CONVEX SET RECOVERING PROCEDURE
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17CHORDAL GRAPH
- No induced cycles of length greater than 3
Intersection graph Subtrees of a tree
Our main result Every g-convex set is the
geodetic closure of its contour
In particular If G(V,E) is chordal, then
ICt(G)V
18CHORDAL GRAPHS ARE PERFECT
What about other perfect families?
f
d
e
c
Ct(G)a,c,f
j
ICt(G)V-j
a
b
g
h
i
G is not perfect
Gid is perfect (comparability)
Gideh is perfect (permutation)
- What about the bipartite family?
19AT-free
perfect
co-comp.
parity
cochordal
comparability
chordal
catval
D.H.
bipartite
str. chordal
trapezoid
permutation
undirected path
directed path
cograph
ptolemaic
split
circular arc
tree
interval
GEODETIC CONTOURS
complete
20Searching for geodetic boundary vertices sets
GRACO 05
- Ignacio M Pelayo, Carmen Hernando, Mercè Mora,
- Carlos Seara Jose Cáceres, M. Luz Puertas
Obrigado Thanks Gracias