Journal of Graph Theory· 2026Q1
Edge‐Coloring a Graph G so That Every Copy of a Graph H Has an Odd Color Class
- 2citations
- Q1SCImago
- 2026year
Short summary
A new graph coloring parameter, denoted $\chi'_o(G, H)$, is introduced, representing the minimum colors needed to edge-color G such that every copy of H has an odd color class. The paper proves $\chi'_o(G, H) \ge \frac{|E(H)|}{|V(H)|}$ and $\chi'_o(G, H) \le 2|V(H)| - 2$.
AI-generated from the title and abstract; the full text is not read.
Key points
- Introduced $\chi'_o(G, H)$: minimum colors for edge-coloring G so every H copy has an odd color class.
- Established lower bound: $\chi'_o(G, H) \ge \frac{|E(H)|}{|V(H)|}$.
- Established upper bound: $\chi'_o(G, H) \le 2|V(H)| - 2$.
- The upper bound result was obtained independently by others.
AI-generated from the title and abstract; the full text is not read.
Abstract
ABSTRACT Recently, Alon introduced the notion of an ‐code for a graph : a collection of graphs on vertex set is an ‐code if it contains no two members whose symmetric difference is isomorphic to . Let denote the maximum possible cardinality of an ‐code, and let . Alon observed that a lower bound on can be obtained by attaining an upper bound on the number of colors needed to edge‐color so that every copy of has an odd color class. Motivated by this observation, we define to be the minimum number of colors needed to edge‐color a graph so that every copy of has an odd color class. We prove and . The first result shows and was obtained independently in [9].
The authors' abstract, as published at the source. Journal of Graph Theory, 2026 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics