论文标题
Digraphs的部分lovász-vextors之间不相等关联的标准
Criteria for the less-equal-relation between partial Lovász-vectors of digraphs
论文作者
论文摘要
使用$ \＃{\ cal H}（g，r）\ leq \＃{\ cal h}（g，s）$研究有限的挖掘$ r $和$ s $ $ \ mathfrak {d}'$是一类有限的挖掘物。结果表明，对于多个类，$ \ mathfrak {d}'$ of Digraphs和$ r \ in \ Mathfrak {d}'$，关系$ \＃{\ cal H}（\ cal H}（g，r）\ leq \ leq \ leq \ leq \ cal H}（\ cal h}（g，s）$ g \ in $ gy by mathak y \ n \ in \ mathak' {\ cal s}（g，r）\ leq \＃{\ cal s}（g，s）$ in \ mathfrak {d}'$，其中$ {\ cal s}（g，h）$是$ g $ g $ g $ g $ g $ g $ g $ g $ g $ h $ popport $ g $ g的$ h $ h $ h $ h $ h $ h.在面向应用程序的规律性条件下，这两个关系甚至是等效的。开发了用于重排的Digraph $ r $的方法，从而导致digraph $ s $，带有$ \＃{\ cal h}（g，r）\ leq \＃{\ cal h}（g，s）$的每个digraph $ g $。该方法应用于构造部分有序的部分集合$ r $和$ s $，并带有$ \＃{\ cal H}（p，r）\ leq \＃{\ cal h}（p，s）$，s in oferted oferted seted设置$ p $。结果的主要部分也适用于无向图。
Finite digraphs $R$ and $S$ are studied with $\# {\cal H}(G,R) \leq \# {\cal H}(G,S)$ for every finite digraph $G \in \mathfrak{ D }'$, where ${\cal H}(G,H)$ is the set of order homomorphisms from $G$ to $H$ and $\mathfrak{ D }'$ is a class of finite digraphs. It is shown that for several classes $\mathfrak{ D }'$ of digraphs and $R \in \mathfrak{ D }'$, the relation $\# {\cal H}(G,R) \leq \# {\cal H}(G,S)$ for every $G \in \mathfrak{ D }'$ is implied by the relation $\# {\cal S}(G,R) \leq \# {\cal S}(G,S)$ for every $G \in \mathfrak{ D }'$, where ${\cal S}(G,H)$ is the set of homomorphisms from $G$ to $H$ mapping all proper arcs of $G$ to proper arcs of $H$. Under an application-oriented regularity condition, the two relations are even equivalent. A method is developed for the rearrangement of a digraph $R$, resulting in a digraph $S$ with $\# {\cal H}(G,R) \leq \# {\cal H}(G,S)$ for every digraph $G$. The method is applied in constructing pairs of partially ordered sets $R$ and $S$ with $\# {\cal H}(P,R) \leq \# {\cal H}(P,S)$ for every partially ordered set $P$. The main part of the results holds also for undirected graphs.
