到图类的满同态
Full homomorphisms to graph classes
AI总结：
该研究围绕极小禁用诱导子图，探究图到阈值图、森林等知名图族的满同态问题，补充了单个蜈蚣图情形的相关研究。
AI中文摘要：
给定图族$\boldsymbol{\textit{F}}$，若图$G$允许到$\boldsymbol{\textit{F}}$中某个图$F$的满同态，则称$G$是满$\boldsymbol{\textit{F}}$-可着色的。我们围绕极小禁用诱导子图研究图何时为满$\boldsymbol{\textit{F}}$-可着色的问题，给出通用结果，可在$\boldsymbol{\textit{F}}$为阈值图、平凡完美图、分裂图、弦图、区间图、强弦图及森林等知名图族时，得到满$\boldsymbol{\textit{F}}$-着色的精确禁用诱导子图族。传统上这类问题针对单个图$H$而非图族研究，受森林图族相关结果启发，我们聚焦于单个蜈蚣图的情形，为该研究领域作出贡献。
英文摘要：
Given a family of graphs $\mathcal{F}$, we define a graph $G$ to be fully $\mathcal{F}$-colourable if $G$ admits a full homomorphism to some $F$ in $\mathcal{F}$. We approach the problem of determining when a graph is fully $\mathcal{F}$-colourable in terms of minimal forbidden induced subgraphs. We provide general results which allow to obtain the exact families of forbidden induced subgraphs for full $\mathcal{F}$-colouring when $\mathcal{F}$ is among some well-known families, such as threshold, trivially perfect, split, chordal, interval and strongly chordal graphs, as well as forests. Traditionally, these questions have been studied for a single graph $H$, not a family. Motivated by our results on the family of forests, we contribute to this research by focusing on the case of a single centipede.
