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Page 53 of Mathematical Reviews Vol. , Issue 2000a [page]

2000 Mathematical Reviews  
irredundant set of a graph G.  ...  In the second part we prove that for claw-free graphs, 6(G) = 6;(G) < sir(G).  ... 

Page 4627 of Mathematical Reviews Vol. , Issue 2000g [page]

2000 Mathematical Reviews  
Summary: “It has been conjectured that the smallest cardinality 8(G) of a perfect neighbourhood set of a graph is bounded above by ir(G), the smallest order of a maximal irredundant set.  ...  In particular the inequality is proved for claw-free graphs and for any graph which has an ir-set S whose induced subgraph has at most six non-isolated vertices.” 2000g:05079 05C35 Erdés, Paul [Erdés,  ... 

Formalization of the Domination Chain with Weighted Parameters (Short Paper)

Daniel E. Severín, Michael Wagner
2019 International Conference on Interactive Theorem Proving  
However, they can be generalized for graphs with weighted vertices where the objective is to maximize/minimize the sum of weights of a set satisfying the same property, and the domination chain still holds  ...  The Cockayne-Hedetniemi Domination Chain is a chain of inequalities between classic parameters of graph theory: for a given graph G, These parameters return the maximum/minimum cardinality of a set satisfying  ...  In particular, this work is the basis to prove later that IR w (defined in the next section) is polynomial on {claw, bull, P 6 , C 6 }-free graphs [12] .  ... 
doi:10.4230/lipics.itp.2019.36 dblp:conf/itp/Severin19 fatcat:2h32nir6irehbpifs3btmf7u74

Author index to volume 231 (2001)

2001 Discrete Mathematics  
Puech, Ramsey properties of generalised irredundant sets in graphs (1}3) 123}134 Diego, I., see F. AguiloH (1}3) 57} 72 Erdo s, P., R.J. Faudree, R.J. Gould, M.S. Jacobson and J.  ...  Rautenbach, On domination and annihilation in graphs with claw-free blocks (1}3) 143}151 Figueroa-Centeno, R.M., R. Ichishima and F.A.  ... 
doi:10.1016/s0012-365x(01)00038-3 fatcat:ynlg7q3jbbcxtlzpc4hjynnruy

List of referees: volumes 191–200

1999 Discrete Mathematics  
Puech, Irredundant and perfect neighborhood sets in graphs and claw-free graphs Fernandez-Merchant, S., see B. Abrego Ferrero, D. and C.  ...  claw-free graphs Brousek, J., Z.Ryjacek and I.  ... 
doi:10.1016/s0012-365x(99)90004-3 fatcat:xbhsnsjfxbcp7llwdhvprlpk6q

Page 5154 of Mathematical Reviews Vol. , Issue 99h [page]

1999 Mathematical Reviews  
Ponomarenko], Compact cellular algebras and permutation groups (247-267); Odile Favaron and Joél Puech, Irredundant and perfect neighborhood sets in graphs and claw-free graphs (269-284); D.  ...  Chang and Min-Jen Jou, The number of maximal independent sets in connected triangle-free graphs (169 178); Gary Chartrand, Frank Harary and Bill Quan Yue, On the out-domination and in-domination numbers  ... 

Master index to volumes 261–270

2003 Discrete Mathematics  
Schelp, Every 3-connected distance claw-free graph is Hamilton-connected 268 (2003) 185-197 Li, R., Hamiltonicity of 3-connected quasi-claw-free graphs (Note) 265 (2003) 393-399 Li, W., Graphs with regular  ...  Zhu, Coloring the square of a K 4 -minor free graph 269 (2003) 303-309 Lindner, C.C., see D.G.  ... 
doi:10.1016/s0012-365x(03)00333-9 fatcat:geqfygze3nef7fqfzbgxdoep6q

An Alternative Method to Crossing Minimization on Hierarchical Graphs

Petra Mutzel
2001 SIAM Journal on Optimization  
A common method for drawing directed graphs is, as a first step, to partition the vertices into a set of k levels and then, as a second step, to permute the vertices within the levels such that the number  ...  MoreoveL we define and investigate the polytope 2/:~S(G) associated with the set of all 2-level planar subgraphs of a given 2-level graph G.  ...  In an irredundant description only facet-defining inequalities are present. An inequality is said to be facet-defining for a polytope P if it is a face of maximal dimension of 7 ).  ... 
doi:10.1137/s1052623498334013 fatcat:7qbe5ufra5a3jcepeqgdgggelm

Master index of volumes 161–170

1997 Discrete Mathematics  
Ryjacek, Claw-free graphs -a survey 164 (1997) 87-147 Favaron, O. and Y.  ...  Lefmann, Canonical partition relations for (m, p, c)-systems Hoffmann, P., Counting maximal cycles in binary matroids (Note) Hoggar, S.G., Weight enumerators of codes derived from polynomial product algorithms  ... 
doi:10.1016/s0012-365x(97)80759-5 fatcat:gk2zgbbx5nbnzbtsvdvo2mkqbi

An alternative method to crossing minimization on hierarchical graphs [chapter]

Petra Mutzel
1997 Lecture Notes in Computer Science  
A common method for drawing directed graphs is, as a rst step, to partition the vertices into a set of k levels and then, as a second step, to permute the vertices within the levels such that the number  ...  Moreover, we de ne and investigate the polytope 2LPS(G) associated with the set of all 2-level planar subgraphs of a given 2-level graph G.  ...  I am very grateful to Ren e Weiskircher for providing the implementation of the branch-and-cut algorithm and for running all the computational experiments.  ... 
doi:10.1007/3-540-62495-3_57 fatcat:e45bozof6jfznpnhz7petptn6m

Master index of volumes 121–130

1994 Discrete Mathematics  
Whitehead, A characterization of graphs of girth eight or more with exactly two sizes of maximal independent sets Finizio, N.J., see Anderson, I.  ...  Youngs, The size of a minimum five-chromatic &-free graph (Note) Harant, J., An upper bound for the radius of a 3-connected graph (Communication) Harary, F., S. Ladrencenko and V.  ... 
doi:10.1016/0012-365x(94)90081-7 fatcat:5c53tthgpjd5fclhixgi3c4bnm

Master index to volumes 251-260

2003 Discrete Mathematics  
Pfender, Pancyclicity in claw-free graphs 256 (2002) 151-160 Goulden, I. and A. Yong, Dyck paths and a bijection for multisets of hook numbers 254 (2002) 153-164 Gouyou-Beauchamps, D., see S.  ...  Tong 260 (2003) 267-273 Li, J., On neighborhood condition for graphs to have ½a; , M.J., Sperner theory in a difference of Boolean lattices 257 (2002) 501-512 Lonc, Z., see M.  ... 
doi:10.1016/s0012-365x(02)00784-7 fatcat:2c4y6lmnybeuxcqr55ngld7r7e

FPT Algorithms for Finding Near-Cliques in c-Closed Graphs [article]

Balaram Behera, Edin Husić, Shweta Jain, Tim Roughgarden, C. Seshadhri
2021 arXiv   pre-print
In this work, we prove that many different kinds of maximal near-cliques can be enumerated in polynomial time (and FPT in c) for c-closed graphs.  ...  (SICOMP 2020) introduced the notion of c-closed graphs and proved that maximal clique enumeration is fixed-parameter tractable with respect to c.  ...  For example, it is known that Maximum Independent Set is NP-hard already for subcubic graphs, and for H-free graphs (for H connected) whenever H is not a path nor a subdivision of the claw (K 1,3 ) [2  ... 
arXiv:2007.09768v4 fatcat:z6eu4ca7orez5cdiexwavuzgg4

Subject Index Volumes 1–200

2001 Discrete Mathematics  
freedom, 4060 of degree n, 5658 claw-center, see claw centre claw-free, see claw free Clay, 2502 clean subdivision of K 3,3 , 5803 cleavage unit, 2360 virtual edge decomposition, 2360 cleaving a planar  ...  graph of paths in a tree , see also enumerative enumeration formula, 1046, 1108, 3577, 4975 for Cayley trees, 1609 for C-permutations, 1609 enumeration function, 578 method, 1195 enumeration of  ...  1574, 2283, 2842, 3609, 4133, 4439, 5612 of a graph, 1574 problem for trees, 4133 (n, k)-graph, 289, 1013, 1574, 3141 with respect to edges, 2962 (n, k)-kernel, 2826, 5138 (n, k)-linear arborific,  ... 
doi:10.1016/s0012-365x(00)00471-4 fatcat:znxg54q6ifgutnhzj3urcw455y

Local search in coding theory

Emile H.L. Aarts, Peter J.M. van Laarhoven
1992 Discrete Mathematics  
For the sake of simplicity and uniformity, all names beginning with articles or prepositions are listed as if written as single words.) Aaltonen, M., A new upper bound on nonbinary block codes 83  ...  Verschut, Pancyclicity of claw-free hamiltonian graphs 197-198 (1-3) (1999) 781-789 Trotter, W.T., see H.A. Kierstead 63 (1987) 217-223 Trotter, W.T., see V.  ...  Whitehead, A characterization of graphs of girth eight or more with exactly two sizes of maximal independent sets 125 (1994) 153-167 Finizio, N.J., see I.  ... 
doi:10.1016/0012-365x(92)90524-j fatcat:sbvlyerdxvdjreaindvnvzrfki
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