Recently, motivated to control a distribution of the vertices having specified degree in a degree factor, the authors introduced a new problem in [Graphs Combin. 39 (2023) #85], which is a degree factor problem of graphs whose vertices are colored with red or blue. In this paper, we continue its research on regular graphs. Among some results, our main theorem is the following: Let $a$, $b$ and $k$ be integers with $1\leq a\leq k\leq b\leq k+a+1$, and let $r$ be a sufficiently large integer compared to $a$, $b$ and $k$. Let $G$ be an $r$-regular graph. We arbitrarily color every vertex of $G$ with red or blue so that no two red vertices are adjacent. Then $G$ has a factor $F$ such that $\deg_{F}(x)\in \{a,b\}$ for every red vertex $x$ and $\deg_{F}(y)\in \{k,k+1\}$ for every blue vertex $y$.
@article{10_37236_12299,
author = {Michitaka Furuya and Mikio Kano},
title = {Degree factors with red-blue coloring of regular graphs},
journal = {The electronic journal of combinatorics},
year = {2024},
volume = {31},
number = {1},
doi = {10.37236/12299},
zbl = {1533.05090},
url = {http://geodesic.mathdoc.fr/articles/10.37236/12299/}
}
TY - JOUR
AU - Michitaka Furuya
AU - Mikio Kano
TI - Degree factors with red-blue coloring of regular graphs
JO - The electronic journal of combinatorics
PY - 2024
VL - 31
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/12299/
DO - 10.37236/12299
ID - 10_37236_12299
ER -
%0 Journal Article
%A Michitaka Furuya
%A Mikio Kano
%T Degree factors with red-blue coloring of regular graphs
%J The electronic journal of combinatorics
%D 2024
%V 31
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/12299/
%R 10.37236/12299
%F 10_37236_12299
Michitaka Furuya; Mikio Kano. Degree factors with red-blue coloring of regular graphs. The electronic journal of combinatorics, Tome 31 (2024) no. 1. doi: 10.37236/12299
