Bipartite coverings and the chromatic number.
Mubayi, Dhruv, Vishwanathan, Sundar (2009)
The Electronic Journal of Combinatorics [electronic only]
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Mubayi, Dhruv, Vishwanathan, Sundar (2009)
The Electronic Journal of Combinatorics [electronic only]
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Jaroslav Ivanco (2007)
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A graph is called magic (supermagic) if it admits a labelling of the edges by pairwise different (and consecutive) positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In the paper we prove that any balanced bipartite graph with minimum degree greater than |V(G)|/4 ≥ 2 is magic. A similar result is presented for supermagic regular bipartite graphs.
Faudree, Jill R., Faudree, Ralph J., Schmitt, John R. (2011)
The Electronic Journal of Combinatorics [electronic only]
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V. A., Ustimenko (2007)
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We have been investigating the cryptographical properties of in nite families of simple graphs of large girth with the special colouring of vertices during the last 10 years. Such families can be used for the development of cryptographical algorithms (on symmetric or public key modes) and turbocodes in error correction theory. Only few families of simple graphs of large unbounded girth and arbitrarily large degree are known. The paper is devoted to the more general theory of directed...