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The maximum number of edges in 2K2-free graphs of bounded degree
1990
Discrete Mathematics
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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
1997
Discrete Mathematics
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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
1993
Journal of Graph Theory
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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
1996
Discrete Mathematics
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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]
2016
arXiv
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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
2004
Discrete Mathematics
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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
1993
Discrete Applied Mathematics
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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
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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
1993
Discrete Applied Mathematics
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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
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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
1987
Journal of Graph Theory
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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]
2021
arXiv
pre-print
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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
2000
Random structures & algorithms (Print)
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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]
2021
arXiv
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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
1985
Journal of computer and system sciences (Print)
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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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