Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized One-to-One Mappings between Homomorphism Sets of Digraphs   Structural properties of finite digraphs $R$ and $S$ are studied which
enforce $\# {\cal H}(G,R) \leq \# {\cal H}(G,S)$ for every finite digraph $G
\in \mathfrak{ D }'$, where ${\cal H}(G,H)$ is the set of homomorphisms from
$G$ to $H$, and $\mathfrak{ D }'$ is a class of digraphs. In a previous study,
we have seen that the key for such a relation between $R$ and $S$ is the
existence of a strong S-scheme from $R$ to $S$. Such an S-scheme $\rho$ defines
a one-to-one mapping $\rho_G : {\cal S}(G,R) \rightarrow {\cal S}(G,S)$ for
every $G \in \mathfrak{ D }'$, where ${\cal S}(G,H)$ is the set of
homomorphisms from $G$ to $H$ mapping proper arcs of $G$ to proper arcs of $H$.
In the present article, we characterize S-schemes $\rho$ which are induced by
strict homomorphisms $\epsilon : {\cal E}(R) \rightarrow {\cal E}(S)$ between
auxiliary systems of $R$ and $S$, and we analyze the mutual dependency between
the properties of $\rho$ and $\epsilon$. Wide applicability of the theory is
ensured by specifying the auxiliary systems ${\cal E}(R)$ and ${\cal E}(S)$ as
EV-systems of $R$ and $S$. The results are applied on a rearrangement method
for digraphs and on undirected graphs.

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The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol