Abstract
A homomorphism of a digraph to another digraph is an edge-preserving vertex mapping. A digraphH is said to be multiplicative if the set of digraphs which do not admit a homomorphism toH is closed under categorical product. In this paper we discuss the multiplicativity of acyclic Hamiltonian digraphs, i.e., acyclic digraphs which contains a Hamiltonian path. As a consequence, we give a complete characterization of acyclic local tournaments with respect to multiplicativity.
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References
J. Bang-Jensen: Locally semicomplete digraphs: a generalization of tournaments,J. Graph Theory,14 (1990), 371–390.
S. Burr, P. Erdős, andL. Lovász: On graphs of Ramsey type,Ars Combinatoria,1 (1976), 167–190.
D. Duffus, B. Sands, andR. Woodrow: On the chromatic number of the product of graphs,J. Graph Theory,9 (1985) 487–495.
H. El-Zahar, andN. Sauer: The chromatic number of the product of two 4-chromatic graphs is 4,Combinatorica,5 (1985), 121–126.
R. Häggkvist, P. Hell, D. J. Miller, andV. Neumann-Lara: On multiplicative graphs and the product conjecture,Combinatorica,8 (1988), 71–81.
A. Hajnal: The chromatic number of the product of two ℵ1 graphs can be countable,Combinatorica,5 (1985), 137–139.
S. Hedetniemi:Homomorphisms and graph automata, University of Michigan Technical Report 03105-44-T, 1966.
P. Hell, H. Zhou, andX. Zhu: Homomorphisms to oriented cycles,Combinatorica,13 (1993), 421–433.
P. Hell, H. Zhou, andX. Zhu: Multiplicativity of oriented cycles,Journal of Combinatorial Theory B,60, No. 2, (1994), 239–253.
J. Nešetřil, andA. Pultr: On classes of relations and graphs determined by subobjects and factor objects,Discrete Mathematics,22, (1978), 287–300.
N. Sauer, andX. Zhu: An approach to Hedetniemi's conjecture,J. Graph Theory,16, 5 (1992), 423–436.
H. Zhou:Homomorphism properties of graph products, Ph.D. thesis, Simon Fraser University, 1988.
H. Zhou: Multiplicativity, part I—variations, multiplicative graphs and digraphs,J. Graph Theory,15 (1991), 469–488.
H. Zhou: Multiplicativity, part II—non-multiplicative digraphs and characterization of oriented paths,J. Graph Theory,15 (1991), 489–509.
H. Zhou: On the non-multiplicativity of oriented cycles,SIAM J. on Discrete Mathematics,5, No. 2 (1992), 207–218.
H. Zhou: Multiplicativity of acyclic digraphs, to appear in Discrete Mathematics.
X. Zhu:Multiplicative structures, Ph.D. thesis, The University of Calgary, 1990.
X. Zhu: A simple proof of the multiplicativity of directed cycles of prime power length,Discrete Applied Mathematics,36 (1992), 313–315.
X. Zhu: On the chromatic number of the products of hypergraphs,Ars Combinatorica.
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Zhou, H., Zhu, X. Multiplicativity of acyclic local tournaments. Combinatorica 17, 135–145 (1997). https://doi.org/10.1007/BF01196137
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DOI: https://doi.org/10.1007/BF01196137