Author

Fahad Panolan

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Preprint Sep 2026

Vertex-Coloring Edge-Weighting: Kernelization and Generalization

An edge weighting of a graph induces a coloring of its vertices in which the color of a vertex is the total weight of the edges incident with it. Such an edge weighting is proper if adjacent vertices always receive distinct colors. Deciding whether a graph admits a proper weighting is known to be NP-complete for the we...

Shubhada Aute, Fahad Panolan, Geevarghese Philip · 0 citations

Preprint Sep 2026

Counting Paths and Trees via Exterior Algebra

We give randomized approximation algorithms for counting k-paths and k-forests in a host graph. Here k denotes the number of pattern vertices, n and m denote the numbers of host vertices and edges or arcs, {\epsilon} is the relative error, and {\delta} is the failure probability. Our main results are: 1. Paths: We appr...

Fahad Panolan, Saket Saurabh, M. Zehavi et al. · 0 citations