TY - JOUR
T1 - Congruences and subdirect representations of graphs
AU - Veldsman, Stefan
N1 - Publisher Copyright:
© 2020 Indonesian Combinatorics Society.
PY - 2020
Y1 - 2020
N2 - A basic tool in universal algebra is that of a congruence. It has been shown that congruences can be defined for graphs with properties similar to their universal algebraic counterparts. In particular, a subdirect product of graphs and hence also a subdirectly irreducible graph, can be expressed in terms of graph congruences. Here the subdirectly irreducible graphs are determined explicitly. Using congruences, a graph theoretic version of the well-known Birkhoff Theorem from universal algebra is given. This shows that any non-trivial graph is a subdirect product of subdirectly irreducible graphs.
AB - A basic tool in universal algebra is that of a congruence. It has been shown that congruences can be defined for graphs with properties similar to their universal algebraic counterparts. In particular, a subdirect product of graphs and hence also a subdirectly irreducible graph, can be expressed in terms of graph congruences. Here the subdirectly irreducible graphs are determined explicitly. Using congruences, a graph theoretic version of the well-known Birkhoff Theorem from universal algebra is given. This shows that any non-trivial graph is a subdirect product of subdirectly irreducible graphs.
KW - Birkhoff's theorem
KW - Congruence on a graph
KW - Quotient graph
KW - Subdirect product of graphs
KW - Subdirectly irreducible graph
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U2 - 10.5614/EJGTA.2020.8.1.9
DO - 10.5614/EJGTA.2020.8.1.9
M3 - Article
AN - SCOPUS:85086723416
SN - 2338-2287
VL - 8
SP - 123
EP - 132
JO - Electronic Journal of Graph Theory and Applications
JF - Electronic Journal of Graph Theory and Applications
IS - 1
ER -