Searching for geodetic boundary vertices sets

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Searching for geodetic boundary vertices sets
GRACO 05

• Ignacio M Pelayo
• Departament de Matemàtica 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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contour
eccentricity
extreme set
boundary
periphery
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f
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
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zz
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zz
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abcdperiphery,contour,eccentricity,boundary
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(ecc(1), ecc(2), ecc(3), ecc(4), ecc(5),
ecc(6))(3,2,2,3,3,2)
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CONVEX SET RECOVERING PROCEDURE
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CHORDAL 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
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CHORDAL 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?

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AT-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
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Searching for geodetic boundary vertices sets
GRACO 05

• Ignacio M Pelayo, Carmen Hernando, Mercè Mora,
• Carlos Seara Jose Cáceres, M. Luz Puertas

Obrigado Thanks Gracias