This paper experimentally evaluates various planar graph drawing algorithms and compares their performance in terms of visual properties.

PlanarBench introduces a novel benchmark to test LLM spatial reasoning by requiring them to draw planar graphs as ASCII art from an edge list, finding that edge count is a stronger difficulty predicto…

The authors map the problem of finding the maximum cut of a planar graph with arbitrary weights to a minimum T-join problem in the absolute dual graph, enabling the use of shortest paths and adapting…

This paper proves that the minimum edge-outerplanarity of a planar graph can be computed in polynomial time.

The paper shows that for non-planar orthogonal drawings of a graph, two drawings are sufficient instead of the planar case's three.

This paper proves that every simple planar graph with no copy of C8 has at most 69/25(n-2) edges, improving the previous bound.

This paper presents approximation algorithms for the one-way directed Reachability-Preserving Minimum Edge Cut problem in directed graphs.

This paper studies the NP-completeness and provides a polynomial-time algorithm for the disjoint separators problem in planar graphs when all sizes are equal to one.

This paper disproves a conjecture about the longest-path lengths of MaxSTN and MinSTN algorithms for producing $st$-orientations of biconnected graphs.

The paper systematically studies the trade-offs between the number of slopes, bends per edge, and required area for planar drawings of bounded-degree graphs, providing new constructions for high-degre…

This paper studies the problem of finding totally disjoint diametral paths in simple connected graphs and provides algorithms for certain classes of graphs.

A new polynomial-time algorithm is presented for optimally coloring perfect graphs using graph-theoretic operations and iterative walk counting.

This paper shows that finding the minimum geodetic set in chordal graphs is fixed parameter tractable, implying a polynomial-time algorithm for k-trees. It also proves that the problem is NP-hard on i…

This paper studies the complexity of the Flood-It game on various graph classes and provides polynomial-time algorithms for Free Flood-It on graphs free of certain jewels, while proving NP-completenes…

This paper presents an algorithmic framework for exhaustively generating and tabulating knot and link diagrams on the thickened torus.

This paper improves the time complexity of exact algorithms for converting a connected graph into a cactus by reducing it from O*(3^n) to O*(2^n) for unweighted graphs, and provides faster algorithms…