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PreprintCC BY 4.0arXiv

Embedding equitable (s,p)-edge-colorings of Kn

  • Stacie Baumann
  • Mika Olufemi
  • Stafford Yerger
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Abstract

An (s,p)-edge-coloring of a graph G is an edge coloring using s colors such that exactly p colors appear at each vertex. To generalize the notion of proper edge-coloring, these colorings are defined to be equitable: the numbers of edges of each color incident to a vertex are fairly distributed. We find the necessary and sufficient conditions for embedding an equitable (s1,p1)-edge-coloring of Kn1 into an equitable (s2,p2)-edge-coloring of Kn2. We focus on the values of n1, p1, n2, and p2 where s1 is necessarily larger than p1 and s2 is necessarily larger than p2.

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Cite

BibTeXRIS
BibTeX
@misc{baumann2026embedding,
  title = {{Embedding equitable (s,p)-edge-colorings of $K_n$}},
  author = {Stacie Baumann and Mika Olufemi and Stafford Yerger},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.07546},
  eprint = {2610.07546},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.07546},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Embedding equitable (s,p)-edge-colorings of K_n
AU  - Stacie Baumann
AU  - Mika Olufemi
AU  - Stafford Yerger
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.07546
UR  - https://arxiv.org/abs/2610.07546
AB  - An (s,p)-edge-coloring of a graph G is an edge coloring using s colors such that exactly p colors appear at each vertex. To generalize the notion of proper edge-coloring, these colorings are defined to be equitable: the numbers of edges of each color incident to a vertex are fairly distributed. We find the necessary and sufficient conditions for embedding an equitable (s_1,p_1)-edge-coloring of K_n_1 into an equitable (s_2,p_2)-edge-coloring of K_n_2. We focus on the values of n_1, p_1, n_2, and p_2 where s_1 is necessarily larger than p_1 and s_2 is necessarily larger than p_2.
ER  -