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Erschienen in:
2012 | OriginalPaper | Buchkapitel
Triangle-Free Outerplanar 3-Graphs Are Pairwise Compatibility Graphs
verfasst von : Sammi Abida Salma, Md. Saidur Rahman
Erschienen in: WALCOM: Algorithms and Computation
Verlag: Springer Berlin Heidelberg
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Given an edge-weighted tree
T
and two non-negative real numbers
d
min
and
d
max
, a
pairwise compatibility graph of T for d
min
and d
max
is a graph
G
= (
V
,
E
), where each vertex
u
′ ∈
V
corresponds to a leaf
u
of
T
and there is an edge (
u
′,
v
′) ∈
E
if and only if
d
min
≤
d
T
(
u
,
v
) ≤
d
max
in
T
. Here,
d
T
(
u
,
v
) denotes the distance between
u
and
v
in
T
, which is the sum of the weights of the edges on the path from
u
to
v
. We call
T
a
pairwise compatibility tree
of
G
. We call a graph
G
a
pairwise compatibility graph
(
PCG
) if there exists an edge-weighted tree
T
and two non-negative real numbers
d
min
and
d
max
such that
G
is a pairwise compatibility graph of
T
for
d
min
and
d
max
. It is known that not all graphs are
PCG
s. Thus it is interesting to know which classes of graphs are
PCG
s. In this paper we show that triangle-free outerplanar graphs with the maximum degree 3 are
PCG
s.