If G is a 2-connected graph of order n with n 5 3A - 2, then G has a cycle containing all vertices of degree A. Our main result is that Conjecture 3 holds under ...
Veldman proved that if G is a 2-connected graph of order n with n ≤ 3k - 2 and |Vk| ≤ k, then G has a cycle containing all vertices of Vk, and it is shown ...
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Cycles containing many vertices of large degree - ScienceDirect
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It is shown that G contains a cycle missing at most max {0, n − 2r} vertices of Vr, yielding a common generalization of a result of Dirac and one of Shi Ronghua ...
Let G be a 2-connected graph on n vertices with maximum degree k where n I3k - 2. We show that there is a cycle in G that contains all vertices of degree k. 0 ...
Oct 1, 2017 · It seems intuitive that the only components obtainable from a graph with degree ≤2 is either a path or a cycle. How does one go about ruling out the other ...
Veldman proved that if G is a 2-connected graph of order n with n ≤ 3k - 2 and |Vk| ≤ k, then G has a cycle containing all vertices of Vk. It is shown that the ...
Here the natural choices are a set of vertices of specified size, a set of vertices satisfying a property (like all vertices of maximum degree or all vertices ...
Nov 20, 2018 · The relationship between the lengths of cycles in a graph and the degrees of its vertices was first studied in a general context by G. A. ...
The cycle C is S-dominating if every vertex in S - V(C) has all its neighbors on C. We denote by C the cycle C with a given orientation, and by C the cycle C ...
Select a vertex v of maximum degree and a (maximal) path P in G v so that the length of P is maximized (over all pairs ًv, Pق). Label the vertices of P as x ¼.