Abstract
In this paper we study the relationship between the binding number and the existence of cycles and complete subgraphs in a given graph. In particular, we prove the following results:
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(i)
If bind(G)≥c≥1 and n>1+c/(c−1)2, then G has a cycle of length 4.
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(ii)
if bind(G)≥3/2, |V(G)|≥5, then G has cycles of length 4 and 5.
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(iii)
If bind(G)≥r−4/3 (where r is an integer not less than 3) then G contains Kr.
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© 1981 Springer-Verlag
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Kane, V.G., Mohanty, S.P. (1981). Binding number, cycles and complete graphs. In: Rao, S.B. (eds) Combinatorics and Graph Theory. Lecture Notes in Mathematics, vol 885. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092273
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DOI: https://doi.org/10.1007/BFb0092273
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-11151-1
Online ISBN: 978-3-540-47037-3
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