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The maximum number of edges in 2K2-free graphs of bounded degree

F.R.K. Chung, A. Gyárfás, Z. Tuza, W.T. Trotter
1990 Discrete Mathematics  
We show that if G is 2K,-free and has maximum degree A(G) = D, then G has at most 5D2/4 edges if D is even. If D is odd, this bound can be improved to (5D* -20 + 1)/4. The extremal graphs are unique.  ...  A graph is 2K,-free if it does not contain an independent pair of edges as an induced subgraph.  ...  The extremal result The main result of this section is the determination of the maximum number of edges in a 2K,-free graph with a given maximum degree.  ... 
doi:10.1016/0012-365x(90)90144-7 fatcat:cxlnrqwjtrfjbjhinetdmkzehe

Maximum induced matchings in graphs

Jiping Liu, Huishan Zhou
1997 Discrete Mathematics  
We provide a formula for the number of edges of a maximum induced matching in a graph.  ...  As applications, we give some structural properties of (k + 1 )K2-free graphs, construct all 2K2-free graphs, and count the number of labeled 2K2-free connected bipartite graphs.  ...  Acknowledgements Many thanks are due to the referees for their valuable comments.  ... 
doi:10.1016/s0012-365x(96)00125-2 fatcat:wszolu3frra3rf7n6i4n3tfji4

LargeP4-free graphs with bounded degree

Myung S. Chung, Douglas B. West
1993 Journal of Graph Theory  
Let ex * (D; H ) denote the maximum number of edges in a connected graph with maximum degree D and no induced subgraph isomorphic to H.  ...  Since any large clique is H-free if H is not a clique, and since disjoint copies of a graph introduce no new connected subgraphs, we define ex*(D; H ) to be the maximum number of edges in a connected H-free  ...  ACKNOWLEDGMENT This research was supported in part by ONR Grant N00014-85K0570 and by the University of Illinois Research Board.  ... 
doi:10.1002/jgt.3190170111 fatcat:wpcdqjfxvzf6jbpwmc2r4ofdp4

Large 2P3-free graphs with bounded degree

Myung S. Chung, Douglas B. West
1996 Discrete Mathematics  
Let ex*(D;H) be the maximum number of edges in a connected graph with maximum degree D and no induced subgraph H; this is finite if and only if H is a disjoint union of paths.  ...  For H = 2P3 (and D ~> 8), the maximum number of edges is ½ [D 4 + D 3 + D 2 + 6D] if D is even and ½ [D 4 + 0 3 + 2D 2 + 3D + 1 ] if D is odd, achieved by a unique extremal graph.  ...  number of edges in a connected graph G with maximum degree at most D.  ... 
doi:10.1016/0012-365x(95)00176-w fatcat:y6wulyzlhzbmnpkejzsujjnl5a

On 2K2-free graphs - Structural and Combinatorial View [article]

S. Dhanalakshmi, N. Sadagopan, V. Manogna
2016 arXiv   pre-print
In this paper, we present the structural characterization of minimal vertex separator and show that there are polynomial number of minimal vertex separators in 2K2-free graphs.  ...  A connected graph is 2K2-free if it does not contain a pair of independent edges as an induced subgraph.  ...  The degree of the vertex v is d G (v) = |N G (v)|. δ(G) and ∆(G) denotes the minimum and maximum degree of a graph G, respectively.  ... 
arXiv:1602.03802v2 fatcat:he4ofde2u5bbhpwxgncpvereui

Boundary classes of graphs for the dominating set problem

Vladimir E Alekseev, Dmitry V Korobitsyn, Vadim V Lozin
2004 Discrete Mathematics  
The notion of a boundary class has been recently introduced as a tool for classiÿcation of hereditary classes of graphs according to the time complexity of NP-hard graph problems.  ...  In the present paper we concentrate on the dominating set problem and obtain three boundary classes for it.  ...  can be found in polynomial time, because the number of maximal cliques in C4-free graphs is bounded by a polynomial in the size of the graph [4] , and hence the algorithm in [9] can generate all of  ... 
doi:10.1016/j.disc.2004.04.010 fatcat:tlcowaiulvfwdlwcvxq5zprguu

On generalized perfect graphs: bounded degree and bounded edge perfection

Edward R. Scheinerman, Ann Trenk
1993 Discrete Applied Mathematics  
Trenk, On generalized perfect graphs: bounded degree and bounded edge perfection, Discrete Applied Mathematics 44 (1993) 2333245.  ...  Acknowledgement The authors would like to thank the referees for valuable suggestions and an improvement in our characterization of XCFperfect graphs.  ...  For a hereditary property 9 we define the P-independence number of G, denoted aY(G), to be the maximum number of vertices in any g-graph induced in G, that is aB(G)=max{I V(H)/: HsG and HEY}.  ... 
doi:10.1016/0166-218x(93)90234-f fatcat:hcb6sb2wevdchpeyncnq5elt4a

Page 7616 of Mathematical Reviews Vol. , Issue 2000k [page]

2000 Mathematical Reviews  
In this paper, we present a number of results on 2-divisible graphs. In particular, we prove that a 2K2- free graph is 2-divisible if and only if it does not contain Cs as an induced subgraph.”  ...  The main result of the paper gives bounds for the least number of edges G can have in the case where G belongs to the class of hypergraphs for which the clique number of I'(G) is bounded independently  ... 

Covering the complete graph with plane cycles

Alan Hartman, Yoav Medan
1993 Discrete Applied Mathematics  
Acknowledgement We would like to thank both the anonymous referees who gave valuable suggestions for the improvement of the presentation.  ...  The size of a G-shuttle cover is the number of shuttles. The rail width of a set of G-shuttles is the maximum over all edges of G of the number of shuttles containing an edge.  ...  Moreover each edge contributes Jo n/2 to the sum. If n ~0 (mod 4) in a cover meeting the bound in (2) then the number of edges in the excess multigraph is not uniquely determined.  ... 
doi:10.1016/0166-218x(93)90239-k fatcat:6e343on3cbf67jw6lvdosz2ale

Page 4067 of Mathematical Reviews Vol. , Issue 97G [page]

1997 Mathematical Reviews  
The author also proves a conjecture of Goodman about the maximum number of monochromatic triangles in any 2-coloring of K,, with a prescribed number of edges in each color.  ...  Let 7 be the graph obtained from the Petersen graph by first deleting a vertex and then contracting an edge incident to a vertex of degree two.  ... 

Extremal problems concerning transformations of the edges of the complete hypergraphs

Yair Caro
1987 Journal of Graph Theory  
We consider extremal problems concerning transformations of the edges of complete hypergraphs.  ...  We estimate the order of the largest subhypergraph K such that for every edge e E €(K), f(e) e f ( K ) , assuming f(e) # e. Several extensions and variations of this problem are also discussed here.  ...  ACKNOWLEDGMENT The author is indebted to both referees for their efforts in simplifying many of the arguments and notatioiis in the paper as well as for their corrections and advice concerning the presentation  ... 
doi:10.1002/jgt.3190110106 fatcat:6edi64u64beofok37lbwszleji

Maximising line subgraphs of diameter at most t [article]

Stijn Cambie, Wouter Cames van Batenburg, Rémi de Joannis de Verclos, Ross J. Kang
2021 arXiv   pre-print
In the case where the graph contains no cycle of length 2t+1, we can improve the bound on the number of edges to one that is exact for t∈{1,2,3,4,6}.  ...  Our main result is that, for any graph of maximum degree Δ with more than 1.5 Δ^t edges, its line graph must have diameter larger than t.  ...  The maximum number of edges in 2K2 -free graphs of bounded degree. Discrete Math., 81(2):129–135, 1990. [8] R. de Joannis de Verclos, R. J. Kang, and L. Pastor.  ... 
arXiv:2103.11898v2 fatcat:v4pbbdbeuzeafmsjmfbg5btcku

The strong chromatic index ofC4-free graphs

Mohammad Mahdian
2000 Random structures & algorithms (Print)  
The strong chromatic index of graphs  ...  It is not hard to see that the maximum number of processors in such a system is equal to the ma.ximum number of edges in a 2&-free graph of maximum degree d. In [SI, it is remarked that D. J.  ...  [14] proved that maximum number of edges of a (k + 1)K2-free graph is k 1 2 .  ... 
doi:10.1002/1098-2418(200010/12)17:3/4<357::aid-rsa9>3.0.co;2-y fatcat:n6u7u555yjhjpczucsqtpwigbi

Tight Ramsey bounds for multiple copies of a graph [article]

Matija Bucic, Benny Sudakov
2021 arXiv   pre-print
The Ramsey number r(G) of a graph G is the smallest integer n such that any 2 colouring of the edges of a clique on n vertices contains a monochromatic copy of G.  ...  More than 30 years ago Burr gave a way of determining c(H), which only applies when the number of copies n is triple exponential in |H|.  ...  We would like to thank Shoham Letzter, Zach Hunter and Domagoj Bradač for careful reading of an early draft of this paper and a number of useful comments and suggestions.  ... 
arXiv:2108.11946v2 fatcat:fvtqnkxpgnbg3l4pp7bnf4lrxu

Scaling algorithms for network problems

Harold N. Garbow
1985 Journal of computer and system sciences (Print)  
Let n, m, and N denote the number of vertices, number of edges, and largest parameter of the network, respectively.  ...  A scaling algorithm for maximum weight matching on a bipartite graph runs in O(n3% log N) time.  ...  ACKNOWLEDGMENTS The author thanks Dr. Robert Tarjan for insightful advice that resulted in new algorithms and better presentation, and Dr. Ann Bateson for many perceptive comments.  ... 
doi:10.1016/0022-0000(85)90039-x fatcat:vzbvscuvtvc5zmmplfgvqergom
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