Search

Start Over Coverage 671-677

1. Homomorphic images of finite subdirectly irreducible unary algebras

Creator:
Ježek, Jaroslav, Marković, P., and Stanovský, David
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
subdirectly irreducible unary algebra
Language:
English
Description:
We prove that a finite unary algebra with at least two operation symbols is a homomorphic image of a (finite) subdirectly irreducible algebra if and only if the intersection of all its subalgebras which have at least two elements is nonempty.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. The contractible subgraph of $5$-connected graphs

Creator:
Qin, Chengfu, Guo, Xiaofeng, and Yang, Weihua
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
5-connected graph, contractible subgraph, and minor minimally $k$-connected
Language:
English
Description:
An edge $e$ of a $k$-connected graph $G$ is said to be $k$-removable if $G-e$ is still $k$-connected. A subgraph $H$ of a $k$-connected graph is said to be $k$-contractible if its contraction results still in a $k$-connected graph. A $k$-connected graph with neither removable edge nor contractible subgraph is said to be minor minimally $k$-connected. In this paper, we show that there is a contractible subgraph in a $5$-connected graph which contains a vertex who is not contained in any triangles. Hence, every vertex of minor minimally $5$-connected graph is contained in some triangle.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public