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تسجيل مستخدم جديدRecognizing embedded caterpillars with weak unit disk contact representations is NP-hard
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Weak unit disk contact graphs are graphs that admit a representation of the nodes as a collection of internally disjoint unit disks whose boundaries touch if there is an edge between the corresponding nodes. We provide a gadget-based reduction to show that recognizing embedded caterpillars that admit a weak unit disk contact representation is NP-hard.
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Weak unit disk contact graphs are graphs that admit representing nodes as a collection of internally disjoint unit disks whose boundaries touch if there is an edge between the corresponding nodes. In this work we focus on graphs without embedding, i.
e., the neighbor order can be chosen arbitrarily. We give a linear time algorithm to recognize whether a caterpillar, a graph where every node is adjacent to or on a central path, allows a weak unit disk contact representation. On the other hand, we show that it is NP-hard to decide whether a tree allows such a representation.
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