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- W4367623662 abstract "For an edge-colored complete graph, we define the color degree of a node as the number of colors appearing on edges incident to it. In this paper, we consider colorings that don't contain tricolored triangles (also called rainbow triangles); these colorings are also called Gallai colorings. We give a complete characterization of all possible color degree sequences $d_1 le d_2 le dots le d_n$ that can arise on a Gallai coloring of $K_n$: it is necessary and sufficient that [ sum_{i = k}^n frac{1}{2^{d_i - d_{k-1}}} ge 1 ] holds for all $1 le k le n$, where $d_0=0$ for convenience. As a corollary, this gives another proof of a 2018 result of Fujita, Li, and Zhang who showed that the minimum color degree in such a coloring is at most $log_2n$." @default.
- W4367623662 created "2023-05-02" @default.
- W4367623662 creator A5019084208 @default.
- W4367623662 date "2023-04-27" @default.
- W4367623662 modified "2023-09-24" @default.
- W4367623662 title "Full Characterization of Color Degree Sequences in Complete Graphs Without Tricolored Triangles" @default.
- W4367623662 doi "https://doi.org/10.48550/arxiv.2304.14579" @default.
- W4367623662 hasPublicationYear "2023" @default.
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