Length of Longest Cycles in a Graph Whose Relative Length is at Least Two
نویسندگان
چکیده
Let G be a graph. We denote p(G) and c(G) the order of a longest path and the order of a longest cycle of G, respectively. Let κ(G) be the connectivity of G, and let σ3(G) be the minimum degree sum of an independent set of three vertices in G. In this paper, we prove that if G is a 2-connected graph with p(G) − c(G) ≥ 2, then either (i) c(G) ≥ σ3(G) − 3 or (ii) κ(G) = 2 and p(G) ≥ σ3(G)− 1. This result implies several known results as corollaries and gives a new lower bound of the circumference.
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ورودعنوان ژورنال:
- Graphs and Combinatorics
دوره 28 شماره
صفحات -
تاریخ انتشار 2012