论文标题
平面$（m，n）$ - 彩色混合图的同态性图
Homomorphisms of planar $(m, n)$-colored-mixed graphs to planar targets
论文作者
论文摘要
a $（m，n）$ - 彩色混合图$ g =（v，a_1，a_2，\ cdots，a_m，e_1，e_1，e_2，\ cdots，e_n）$是具有$ m $ $ $ $ $ $ $ n $ colors的颜色的图形。我们不允许两个弧形或边缘具有相同的端点。来自$（m，n）$ - 彩色混合图$ g $到另一$（m，n）$ - 彩色混合图$ h $的同构形态是一种形态$φ：v（g）\ rightarrow v（h）$，这样的每个边缘（resp。g$ g $ of $ g $）映射到$ g $的$ g $（均为$ h $ h $ h $ h $ h $ he of and of and of and of and of of of of of。 a $（m，n）$ - 彩色混合图$ t $被称为$ p_g^{（m，n）} $ - 如果$ p_g^{（m，n）} $中的每个图中的每个图）（平面$（m，n）$ - 彩色 - 彩色 - 彩色混合图，至少是g $ g $），至少是$ g $）。 我们表明，平面$ p_g^{（m，n）} $ - 通用图并不存在，以$ 200M+n \ ge3 $（和$ g $的任何值），并找到最小（在数字顶点）平面$ p_g^{（m，n）} $ - 在其他情况下的通用图。
An $(m, n)$-colored-mixed graph $G=(V, A_1, A_2,\cdots, A_m, E_1, E_2,\cdots, E_n)$ is a graph having $m$ colors of arcs and $n$ colors of edges. We do not allow two arcs or edges to have the same endpoints. A homomorphism from an $(m,n)$-colored-mixed graph $G$ to another $(m, n)$-colored-mixed graph $H$ is a morphism $φ:V(G)\rightarrow V(H)$ such that each edge (resp. arc) of $G$ is mapped to an edge (resp. arc) of $H$ of the same color (and orientation). An $(m,n)$-colored-mixed graph $T$ is said to be $P_g^{(m, n)}$-universal if every graph in $P_g^{(m, n)}$ (the planar $(m, n)$-colored-mixed graphs with girth at least $g$) admits a homomorphism to $T$. We show that planar $P_g^{(m, n)}$-universal graphs do not exist for $2m+n\ge3$ (and any value of $g$) and find a minimal (in the number vertices) planar $P_g^{(m, n)}$-universal graphs in the other cases.
