𝔖 Bobbio Scriptorium
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On the coverings of graphs

✍ Scribed by F.R.K. Chung


Publisher
Elsevier Science
Year
1980
Tongue
English
Weight
383 KB
Volume
30
Category
Article
ISSN
0012-365X

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In this paper it is proved that the exponential generating function of the numbers, denoted by N(p, q), of irreducible coverings by edges of the vertices of complete bipartite graphs Kp.q equals exp(xe r + ye x -x -y -xy) -t.

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## Abstract We give a 4‐chromatic planar graph, which admits a vertex partition into three parts such that the union of every two of them induces a forest. This solves a problem posed by BΓΆhme. Also, by constructing an infinite sequence of graphs, we show that the cover degeneracy can be arbitraril

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Let G be a line graph. Orlin determined the clique covering and clique partition numbers cc(G) and cp(G). We obtain a constructive proof of Orlin's result and in doing so we are able to completely enumerate the number of distinct minimal clique covers and partitions of G, in terms of easily calculab