Independent cycles and chorded cycles in graphs
نویسندگان
چکیده
In this paper, we investigate sufficient conditions on the neighborhood of independent vertices which imply that a graph contains k independent cycles or chorded cycles. This is related to several results of Corrádi and Hajnal, Justesen, Wang, and Faudree and Gould on graphs containing k independent cycles, and Finkel on graphs containing k chorded cycles. In particular, we establish that if independent vertices in G have neighborhood union at least 2k+ 1, then G has k chorded cycles, so long as |G| > 30k, and settling a conjecture of and improving a result of Faudree and Gould, who establish that 3k suffices. Additionally, we show that a graph with neighborhood union of independent vertices at least 4k + 1 has at least k chorded cycles; Finkel previously established that minimum degree 3k was also a sufficient condition for this.
منابع مشابه
Chorded Cycles
A chord is an edge between two vertices of a cycle that is not an edge on the cycle. If a cycle has at least one chord, then the cycle is called a chorded cycle, and if a cycle has at least two chords, then the cycle is called a doubly chorded cycle. The minimum degree and the minimum degree-sum conditions are given for a graph to contain vertex-disjoint chorded (doubly chorded) cycles containi...
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