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Neighborhood unions and hamiltonicity of graphs

Ruqun Shen, Feng Tian
1995 Discrete Mathematics  
subgraph of a graph in one of three families of exceptional graphs.  ...  Let G be a graph of order n.  ...  Acknowledgements The authors wish to thank the anonymous referees for their helpful suggestions and comments.  ... 
doi:10.1016/0012-365x(93)00181-4 fatcat:imv55sybj5akpbz4vcwqnsbqhu

The neighborhood union of independent sets and hamiltonicity of graphs

Guantao Chen, Xuechao Li, Zhengsheng Wu, Xingping Xu
2007 Discrete Mathematics  
Let G be a graph, N (u) the neighborhood of u for each u ∈ V (G), and N(U) = u∈U N(u) for each U ⊆ V (G).  ...  For any two positive integers s and t, we prove that there exists a least positive integer N(s, t) such that every (s + t)-connected graph G of order n N(s, t) is hamiltonian if |N(S)| + |N(T )| n for  ...  For any v ∈ V (G), let N(v) := {w : vw ∈ E(G)} and d(v) := |N(v)|, where N(v) is called the neighborhood of v and d(v) is called the degree of v, respectively.  ... 
doi:10.1016/j.disc.2006.10.010 fatcat:3ogwfqncrnhzbafvsuhibrx7qu

Neighborhood Union Conditions for Hamiltonicity of P 3-Dominated Graphs

Xiaoling Ma, Elkin Vumar
2013 Graphs and Combinatorics  
Meanwhile, their neighborhood union conditions for hamiltonicity of P 3 -dominated graphs are also different.  ...  A cycle containing all the vertices of the graph is said to be a Hamilton cycle. A graph containing a Hamilton cycle is said to be hamiltonian.  ...  This can be seen from the P 3dominated graph G obtained as follows: take three copies of the complete graph K t , say, K 1 t , K 2 t and K 3 t (t ≥ 3), pick 2 distinct vertices x i , y i from K i t (i  ... 
doi:10.1007/s00373-013-1354-4 fatcat:66a3fbbntrdbfmairfpapa5ela

Page 4752 of Mathematical Reviews Vol. , Issue 92i [page]

1992 Mathematical Reviews  
{For the entire collection see MR 92f:05006.} 92i:05141 05C45 Jackson, Bill (4-LNDG) Neighborhood unions and Hamilton cycles. J. Graph Theory 15 (1991), no. 4, 443-451.  ...  Summary: “For sets of vertices, we consider a form of generalized degree based on neighborhood unions.  ... 

New Perspectives on Neighborhood-Prime Labelings of Graphs [article]

John Asplund, N. Bradley Fox, Arran Hamm
2018 arXiv   pre-print
In this paper, we introduce techniques for finding neighborhood-prime labelings based on the Hamiltonicity of the graph, by using conditions on possible degrees of vertices, and by examining a neighborhood  ...  In addition, we show that almost all graphs and almost all regular graphs have are neighborhood-prime, and we find all graphs of order 10 or less that have a neighborhood-prime labeling.  ...  Since for any tree T , the neighborhood-prime graph of T is a forest, the following result is a consequence of Theorem 31 and since a prime graph is still prime after having an edge deleted.  ... 
arXiv:1804.02473v1 fatcat:vwlvxarlozhr5p54wr3eouih7i

A New Property of Hamilton Graphs [article]

Heping Jiang
2015 arXiv   pre-print
Hamilton graphs as being a necessary and sufficient condition characterized in the connectivity of the subgraph that induced from the cycle structure of a given graph.  ...  A Hamilton cycle is a cycle containing every vertex of a graph. A graph is called Hamiltonian if it contains a Hamilton cycle.  ...  Generally speaking, for a given (N 3 , N 2 , N 1 )-free subgraph of a Hamilton graph G, we could obtain a set of cycles by removing some cycles from it, and the union of these cycles yields a Hamilton  ... 
arXiv:1508.00068v1 fatcat:pevd37rb5vcp5jrw7a6mbch5u4

Contents

2007 Discrete Mathematics  
Seneviratne Codes from the line graphs of complete multipartite graphs and PD-sets 2217 G. Chen, X. Li, Z.Wu and X. Xu The neighborhood union of independent sets and hamiltonicity of graphs 2226 J.I.  ...  Kennedy and A. Steinberg Odd neighborhood transversals on grid graphs 2200 M. Blidia, M. Chellali, O. Favaron and N. Meddah On k-independence in graphs with emphasis on trees 2209 J.D. Key and P.  ... 
doi:10.1016/s0012-365x(07)00448-7 fatcat:frwe7pcm2rgmjl5o3kc6k4hqte

Page 5926 of Mathematical Reviews Vol. , Issue 92k [page]

1992 Mathematical Reviews  
Various degree and neighborhood conditions are shown to imply long cycles in a graph, and some of these new conditions are shown to generalize well-known conditions for Hamiltonicity of a graph.  ...  a Hamiltonian cycle) and the previous result on neighborhood unions.  ... 

The γ-neighborhood graph

Remco C. Veltkamp
1992 Computational geometry  
., The y-neighborhood graph, Computational Geometry: Theory and Applications 1 (1992) 227-246. This paper presents a novel two-parameter geometric graph, the y-neighborhood graph.  ...  This graph unifies a number of geometric graphs such as the convex hull, the Delaunay triangulation, and in 2D also the Gabriel graph and the circle-based P-skeleton, into a continuous spectrum of geometric  ...  Especially when the neighborhood is the union of these spheres, the y-graph is more like (a part of) a tesselation.  ... 
doi:10.1016/0925-7721(92)90003-b fatcat:si42dp4x5bch7fvkeo4am72kym

Page 636 of Mathematical Reviews Vol. , Issue 92b [page]

1992 Mathematical Reviews  
In this paper the authors correlate the neighborhood union to the length of dominating cycles and paths.  ...  (NL-TWEN-A) Long dominating cycles and paths in graphs with large neighborhood unions. J. Graph Theory 15 (1991), no. 1, 29-38. Recently, R. J. Faudree, R. J. Gould, the reviewer and R. H. Schelp [J.  ... 

Page 2018 of Mathematical Reviews Vol. , Issue 96d [page]

1996 Mathematical Reviews  
Here n is the size of the two vertex classes X¥ and Y, and A is the minimum edge density, over all nontrivial partitions of ¥ and Y into 4, X — A, B and Y — B, of the graph comprising the union of the  ...  Having a SVEN is equivalent to every induced subgraph of G having a split vertex and these are the split neighborhood graphs of the title. The principal result of this paper is that split neighborhood  ... 

Page 3589 of Mathematical Reviews Vol. , Issue 92g [page]

1992 Mathematical Reviews  
If G is a graph and x a vertex of G, let the neighborhood N(x) of x be the set of vertices of G adjacent to x. The degree d(x) = |N(x)|.  ...  [Li, Hao"] (PRC-ASBJ-S) Hamiltonism, degree sum and neighborhood intersections. Discrete Math. 90 (1991), no. 1, 41-52.  ... 

An O(n) time algorithm for finding Hamilton cycles with high probability [article]

Rajko Nenadov, Angelika Steger, Pascal Su
2020 arXiv   pre-print
We design a randomized algorithm that finds a Hamilton cycle in 𝒪(n) time with high probability in a random graph G_n,p with edge probability p≥ C log n / n.  ...  This closes a gap left open in a seminal paper by Angluin and Valiant from 1979.  ...  Similarly, the d-neighborhood of a set of vertices S, denoted by N d (S), is defined as the union of the d-neighborhoods of all vertices in S.  ... 
arXiv:2012.02551v1 fatcat:beqy7fzsxzfpvcjudmcglmtnnm

Degree-doubling graph families [article]

János Körner, Irene Muzi
2012 arXiv   pre-print
Let G be a family of n-vertex graphs of uniform degree 2 with the property that the union of any two member graphs has degree four.  ...  We determine the leading term in the asymptotics of the largest cardinality of such a family. Several analogous problems are discussed.  ...  Here the union of two graphs on the same vertex set is the graph whose edge set is the union of those of the two graphs.  ... 
arXiv:1208.1963v1 fatcat:u2udlbk3tfb6binlly75hojhq4

Degree-Doubling Graph Families

János Körner, Irene Muzi
2013 SIAM Journal on Discrete Mathematics  
Let G be a family of n-vertex graphs of uniform degree 2 with the property that the union of any two member graphs has degree four.  ...  We determine the leading term in the asymptotics of the largest cardinality of such a family. Several analogous problems are discussed.  ...  Here the union of two graphs on the same vertex set is the graph whose edge set is the union of those of the two graphs.  ... 
doi:10.1137/120887242 fatcat:ugbctvlrkbfh7md4e7poex4qeq
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