论文标题
独特的$ d $ - 彩色的digraphs具有大围栏II：通过概括简化
Uniquely $D$-colourable digraphs with large girth II: simplification via generalization
论文作者
论文摘要
We prove that for every digraph $D$ and every choice of positive integers $k$, $\ell$ there exists a digraph $D^*$ with girth at least $\ell$ together with a surjective acyclic homomorphism $ψ\colon D^*\to D$ such that: (i) for every digraph $C$ of order at most $k$, there exists an acyclic homomorphism $ d^*\ to C $，并且仅当存在一个无环同构$ d \ to c $时； （ii）对于最多$ k $的每$ d $ d $ digraph $ c $ c $ c $ c $，每一个无循环同构$φ\ colon d^*\ c $ to c $都存在独特的无循环同型同构$ f \ colon d \ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c = f \ circim courcim = f \ circi \ circin光。这意味着[A。 Harutyunyan等人，独特的$ d $ - 彩色的Digraphs，带有巨大的腰带，加拿大。 J. Math。，64（6）（2012），1310-1328; MR2994666]与该工作的工作方式类似[J. Nešet松和X.理论ser。 B，90（1）（2004），161-172; MR2041324]概括并扩展[X。 Zhu，独特的$ h $ - 可油的图形，带有大围栏，J。GraphDoemon，23（1）（1996），33-41; MR1402136]。
We prove that for every digraph $D$ and every choice of positive integers $k$, $\ell$ there exists a digraph $D^*$ with girth at least $\ell$ together with a surjective acyclic homomorphism $ψ\colon D^*\to D$ such that: (i) for every digraph $C$ of order at most $k$, there exists an acyclic homomorphism $D^*\to C$ if and only if there exists an acyclic homomorphism $D\to C$; and (ii) for every $D$-pointed digraph $C$ of order at most $k$ and every acyclic homomorphism $φ\colon D^*\to C$ there exists a unique acyclic homomorphism $f\colon D\to C$ such that $φ=f\circψ$. This implies the main results in [A. Harutyunyan et al., Uniquely $D$-colourable digraphs with large girth, Canad. J. Math., 64(6) (2012), 1310-1328; MR2994666] analogously with how the work [J. Nešetřil and X. Zhu, On sparse graphs with given colorings and homomorphisms, J. Combin. Theory Ser. B, 90(1) (2004), 161-172; MR2041324] generalizes and extends [X. Zhu, Uniquely $H$-colorable graphs with large girth, J. Graph Theory, 23(1) (1996), 33-41; MR1402136].
