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The bichromaticity of a lattice-graph

Published online by Cambridge University Press:  09 April 2009

Frank Harary ,
Derbiau Hsu  and
Zevi Miller
Zevi Miller
Affiliation:
University of Michigan, Ann Arbor, Michigan, U.S.A.
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Abstract

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The bichromaticity β(B) of a bipartite graph B has been defined as the maximum order of a complete bipartite graph onto which B is homomorphic. This number was previously determined for trees and even cycles. It is now shown that for a lattice-graph Pm × Pm the cartesian product of two paths, the bichromaticity is 2 + {mn/2}.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 3 , May 1977 , pp. 354 - 359
Copyright
Copyright © Australian Mathematical Society 1977

References

Harary, F. (1969), Graph Theory (Addison-Wesley, Reading, Mass.)CrossRefGoogle Scholar
Harary, F. and Hedetniemi, S. T. (1970), ‘The achromatic number of a graph’, J. Combinatorial Theory, 8, 154–161.CrossRefGoogle Scholar
Harary, F., Hsu, D., and Miller, Z. (1977), ‘The bichromaticity of a tree’, Theory and Applications of Graphs — in America's. Bicentennial Year. (Alavi, Y. and Lick, D. R., eds.), (Springer-Verlag, Berlin.)Google Scholar