Hardness of Planarity for Weak Temporal Sequences of 2-Connected Graphs

TL;DR

This paper proves that deciding whether a sequence of 2-connected graphs can be simultaneously embedded in a plane, under a specific weak deletion relation, is an NP-hard problem, highlighting its computational difficulty.

Contribution

It establishes the NP-hardness of the simultaneous planarity problem for weak deletion sequences of 2-connected graphs, a previously unresolved complexity question.

Findings

Determined the NP-hardness of the problem.

Focused on weak deletion sequences of 2-connected graphs.

Contributed to understanding the complexity of graph embedding problems.

Abstract

A weak deletion sequence is a sequence $(G_1,\ldots,G_n)$ of graphs so that for each $i\in[n-1]$ either $G_i$ is isomorphic to a subgraph of $G_{i+1}$, or vice versa: $G_{i+1}$ is isomorphic to a subgraph of $G_i$. We prove that determining the simultaneous planar embeddability of weak deletion sequences of $2$-connected graphs is NP-hard.