Hoffman-London Graphs: Paths Minimize H-Colorings in Trees
Research Paper#Graph Theory, Combinatorics🔬 Research|Analyzed: Jan 3, 2026 18:27•
Published: Dec 29, 2025 19:50
•1 min read
•ArXivAnalysis
This paper introduces a new technique using automorphisms to analyze and minimize the number of H-colorings of a tree. It identifies Hoffman-London graphs, where paths minimize H-colorings, and provides matrix conditions for their identification. The work has implications for various graph families and provides a complete characterization for graphs with three or fewer vertices.
Key Takeaways
- •Introduces the concept of Hoffman-London graphs.
- •Develops a new technique using automorphisms to analyze H-colorings.
- •Provides matrix conditions for identifying Hoffman-London graphs.
- •Applies the technique to identify several families of Hoffman-London graphs.
- •Fully characterizes minimizing trees for graphs with three or fewer vertices.
Reference / Citation
View Original"The paper introduces the term Hoffman-London to refer to graphs that are minimal in this sense (minimizing H-colorings with paths)."