论文标题
Digraphs的部分lovás-vectors之间不相等相关的相互依存关系
Interdependencies of less-equal-relations between partial Lovász-vectors of digraphs
论文作者
论文摘要
对于Digraphs $ g $和$ h $，让$ {\ cal H}（g，h）$是从$ g $到$ h $的所有同构的集合，让$ {\ cal s}（g，h）$是这些同构的子集，这些同构的子集中映射了$ g $ g $ in $ g $ in $ h $ h $ h $ h $ h $ h $。从较早的调查中，我们知道，对于某些digraphs $ r $和$ s $，关系“ $ \＃{\ cal s}（g，g，r）\ leq \＃{\ cal s}（\ cal s}（g，s）$ for ALL $ g \ in \ Mathfrak in \ Mathfrak {d} h}（g，s）$ for \ in \ mathfrak {d}'$''，其中$ \ mathfrak {d}'$是Digraphs的子类。现在，我们要求逆：digraphs $ r，s $以及digraphs的$ \ mathfrak {d}'$ of Digraphs的$ dik“ $ \＃” s}（g，r）\ leq \＃{\ cal s}（g，s）$ for \ in \ mathfrak in \ mathfrak {d}'$“？”？我们证明了对Digraph类的三种组合的含义。特别是，与所有平面posets $ g $相对于所有平面posets $ r，s $的关系是等效的。
For digraphs $G$ and $H$, let ${\cal H}(G,H)$ be the set of all homomorphisms from $G$ to $H$, and let ${\cal S}(G,H)$ be the subset of those homomorphisms mapping all proper arcs in $G$ to proper arcs in $H$. From an earlier investigation we know that for certain digraphs $R$ and $S$, the relation "$\# {\cal S}(G,R) \leq \# {\cal S}(G,S)$ for all $G \in \mathfrak{ D }'$" implies "$\# {\cal H}(G,R) \leq \# {\cal H}(G,S)$ for all $G \in \mathfrak{ D }'$", where $\mathfrak{ D }'$ is a subclass of digraphs. Now we ask for the inverse: For which digraphs $R, S$ and which subclasses $\mathfrak{ D }'$ of digraphs does "$\# {\cal H}(G,R) \leq \# {\cal H}(G,S)$ for all $G \in \mathfrak{ D }'$" imply "$\# {\cal S}(G,R) \leq \# {\cal S}(G,S)$ for all $G \in \mathfrak{ D }'$"? We prove this implication for three combinations of digraph classes. In particular, the relations are equivalent for all flat posets $R, S$ with respect to all flat posets $G$.
