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On rectangle intersection graphs with stab number at most two
Discrete Applied Mathematics ( IF 1.1 ) Pub Date : 2021-01-01 , DOI: 10.1016/j.dam.2020.11.003
Dibyayan Chakraborty , Sandip Das , Mathew C. Francis , Sagnik Sen

Abstract Rectangle intersection graphs are the intersection graphs of axis-parallel rectangles in the plane. A graph G is said to be a k -stabbable rectangle intersection graph, or k -SRIG for short, if it has a rectangle intersection representation in which k horizontal lines can be placed such that each rectangle intersects at least one of them. In this article, we introduce some natural subclasses of 2-SRIG and study the containment relationships among them. It is shown that one of these subclasses can be recognized in linear-time if the input graphs are restricted to be triangle-free. We also make observations about the chromatic number of 2-SRIGs. It is shown that the Chromatic Number problem is NP-complete for 2-SRIGs, by showing that the problem is NP-complete for 2-row B 0 -VPGs. This is a strengthening of some known results from the literature.

中文翻译:

在插入数最多为两个的矩形交点图上

摘要 矩形相交图是平面内平行轴的矩形的相交图。如果图 G 具有矩形相交表示,其中可以放置 k 条水平线,使得每个矩形至少与其中的一条相交,则称该图 G 是 ak -stabbable 矩形相交图,或简称为 k -SRIG。在本文中,我们介绍了 2-SRIG 的一些自然子类,并研究了它们之间的包含关系。结果表明,如果输入图被限制为无三角形,则可以在线性时间内识别这些子类之一。我们还观察了 2-SRIG 的色数。通过表明该问题对于 2 行 B 0 -VPG 是 NP 完全的,表明色数问题对于 2-SRIG 是 NP 完全的。
更新日期:2021-01-01
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