Independent cycles and chorded cycles in graphs
نویسندگان
چکیده
منابع مشابه
Independent cycles and chorded cycles in graphs
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 in...
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Very recently, Bialostocki et al. proposed the following conjecture. Let r, s be two nonnegative integers and let G = (V (G), E(G)) be a graph with |V (G)| ≥ 3r + 4s and minimum degree δ(G) ≥ 2r + 3s. Then G contains a collection of r cycles and s chorded cycles, all vertex-disjoint. We prove that this conjecture is true.
متن کاملDisjoint chorded cycles in graphs
We propose the following conjecture to generalize results of Pósa and Corrádi Hajnal. Let r, s be nonnegative integers and let G be a graph with |V (G)| ≥ 3r + 4s and minimal degree δ(G) ≥ 2r + 3s. Then G contains a collection of r + s vertex disjoint cycles, s of them with a chord. We prove the conjecture for r = 0, s = 2 and for s = 1. The corresponding extremal problem, to find the minimum n...
متن کاملOn independent doubly chorded cycles
In a graph G, we say a cycle C : v1, v2, . . . , vk, v1 is chorded if its vertices induce an additional edge (chord) which is not an edge of the cycle. The cycle C is doubly chorded if there are at least two such chords. In this paper we show a sharp degree sum condition that implies the existence of k vertex disjoint doubly chorded cycles in a graph. © 2015 Elsevier B.V. All rights reserved.
متن کاملChorded 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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ژورنال
عنوان ژورنال: Journal of Combinatorics
سال: 2013
ISSN: 2156-3527,2150-959X
DOI: 10.4310/joc.2013.v4.n1.a6