Year: 2025
Type: preprint
Abstract: In this paper, we introduce the concept of bikernel by monochromatic paths of a bicolored digraph. This concept is strongly motivated by the existing notions of kernels, kernels by monochromatic paths, and double stable augmented categories. We establish sufficient and necessary conditions for several families of bicolored digraphs to have a bikernel by monochromatic paths. Also, we characterize bicolored digraphs without monochromatic cycles that possess a bikernel by monochromatic paths. Similarly, we characterize bicolored digraphs with monochromatic cycles that also have a bikernel by monochromatic paths. Furthermore, we prove sufficient and necessary conditions for some families of digraphs to be $BK$-colorable. This means that a bicoloration of the digraph exists where the resulting bicolored digraph has a bikernel.
Source: arXiv (Cornell University)
Authors: Diaz-Diaz, Dennis J., de-la-Fuente-Jimenez, Isaías F., Hoekstra-Mendoza, Teresa I., Licona-Velázquez, Miguel E., Terrones-Segura, Victoria
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6891908140
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