KLX is the min-max congestion of open back edges over DFS traversals; graphs with KLX at most 2 are fully characterized with linear-time recognition, any graph has tree-width at most KLX+1, and KLX ≤ k is MSO2-expressible hence linear-time decidable for fixed k.
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Saddle-point asymptotics for chromatic and Tutte polynomials of complete multipartite graphs prove Kotesovec's fixed-column conjecture and yield fixed-part and all-order expansions for OEIS sequences.
Polynomial kernels exist for Leaf & Internal-Constrained Diverse Spanning Trees (parameter p+q+k+ℓ) and Leaf & Non-terminal-Constrained Diverse Spanning Trees (parameter p+|V_NT|+k+ℓ).
RLGT is a modular reinforcement learning framework for extremal graph theory that handles undirected, directed, looped, and multi-colored graphs to facilitate future research.
Segmentedness is defined as the complement of edge density in the policy graph, with a sampling-based estimator requiring only 97 random node pairs for a 95% confidence interval of width ±0.2 independent of network size.
citing papers explorer
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A Congestion Parameter for Depth-First Graph Traversals
KLX is the min-max congestion of open back edges over DFS traversals; graphs with KLX at most 2 are fully characterized with linear-time recognition, any graph has tree-width at most KLX+1, and KLX ≤ k is MSO2-expressible hence linear-time decidable for fixed k.
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Saddle-Point Asymptotics for Chromatic and Tutte Polynomial Evaluations of Complete Multipartite Graphs
Saddle-point asymptotics for chromatic and Tutte polynomials of complete multipartite graphs prove Kotesovec's fixed-column conjecture and yield fixed-part and all-order expansions for OEIS sequences.
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Polynomial Kernels for Spanning Tree with Diversity Requirements
Polynomial kernels exist for Leaf & Internal-Constrained Diverse Spanning Trees (parameter p+q+k+ℓ) and Leaf & Non-terminal-Constrained Diverse Spanning Trees (parameter p+|V_NT|+k+ℓ).
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RLGT: A reinforcement learning framework for extremal graph theory
RLGT is a modular reinforcement learning framework for extremal graph theory that handles undirected, directed, looped, and multi-colored graphs to facilitate future research.
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How segmented is my network?
Segmentedness is defined as the complement of edge density in the policy graph, with a sampling-based estimator requiring only 97 random node pairs for a 95% confidence interval of width ±0.2 independent of network size.