Abstract
AbstractA graph $$G = (V,E)$$
G
=
(
V
,
E
)
is a double-threshold graph if there exist a vertex-weight function $$w :V \rightarrow \mathbb {R}$$
w
:
V
→
R
and two real numbers $$\mathtt {lb}, \mathtt {ub}\in \mathbb {R}$$
lb
,
ub
∈
R
such that $$uv \in E$$
u
v
∈
E
if and only if $$\mathtt {lb}\le \mathtt {w}(u) + \mathtt {w}(v) \le \mathtt {ub}$$
lb
≤
w
(
u
)
+
w
(
v
)
≤
ub
. In the literature, those graphs are studied also as the pairwise compatibility graphs that have stars as their underlying trees. We give a new characterization of double-threshold graphs that relates them to bipartite permutation graphs. Using the new characterization, we present a linear-time algorithm for recognizing double-threshold graphs. Prior to our work, the fastest known algorithm by Xiao and Nagamochi [Algorithmica 2020] ran in $$O(n^{3} m)$$
O
(
n
3
m
)
time, where n and m are the numbers of vertices and edges, respectively.
Funder
Japan Society for the Promotion of Science
Core Research for Evolutional Science and Technology
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computer Science Applications,General Computer Science
Cited by
2 articles.
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