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Քուլաքզյան Մ., Նիկողոսյան Ժ., Кулакзян М., Никогосян Ж.
Title:
Two Generalized Lower Bounds for the Circumference
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Creator:
Mossine S. Koulakzian ; Zhora G. Nikoghosyan
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Uncontrolled Keywords:
Circumference ; Minimum degree ; Degree sums.
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Abstract:
In 2013, the second author obtained two lower bounds for the length of a longest cycle C in a graph G in terms of the length of a longest path (a longest cycle) in G¡C and the minimum degree of G (Zh.G. Nikoghosyan, "Advanced Lower Bounds for the Circumference", Graphs and Combinatorics 29, pp. 1531-1541, 2013). In this paper we present two analogous bounds based on the average of the first i smallest degrees in G - C for appropriate i instead of the minimum degree.