Advances in Graph Theory and Algorithms

The field of graph theory and algorithms is rapidly advancing, with a focus on developing new techniques and tools for analyzing and solving complex graph problems. Recent research has centered on improving the efficiency and efficacy of algorithms for tasks such as graph coloring, connectivity, and motif parameter counting. Notably, new methods for computing planar H-modulators and parametric extensions have been introduced, enabling the solution of various graph problems in polynomial time. Additionally, researchers have made progress in the study of graph embeddings, including the development of a discrete analog of Tutte's barycentric embeddings on surfaces. Furthermore, advances have been made in the area of distributed graph sketching, with new lower bounds established for deciding graph connectivity problems. Some papers are particularly noteworthy, including the introduction of H-Planarity and parametric extensions, which enable the solution of various graph problems in polynomial time. The paper on a fast coloring oracle for average case hypergraphs presents a new simple and elementary deterministic 2-coloring algorithm and a randomized one with average expected running time of only O(n).

Sources

H-Planarity and Parametric Extensions: when Modulators Act Globally

Paths and Intersections: Exact Emulators for Planar Graphs

A Fast Coloring Oracle for Average Case Hypergraphs

On maximal curves of $n$-correct sets

Deterministic Lower Bounds for $k$-Edge Connectivity in the Distributed Sketching Model

Which graph motif parameters count?

A Discrete Analog of Tutte's Barycentric Embeddings on Surfaces

Kernelization for $H$-Coloring

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