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

2019
*
International Conference on Interactive Theorem Proving
*

However, they can be generalized

doi:10.4230/lipics.itp.2019.36
dblp:conf/itp/Severin19
fatcat:2h32nir6irehbpifs3btmf7u74
*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] . ...##
###
Author index to volume 231 (2001)

2001
*
Discrete Mathematics
*

Puech, Ramsey properties

doi:10.1016/s0012-365x(01)00038-3
fatcat:ynlg7q3jbbcxtlzpc4hjynnruy
*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. ...##
###
List of referees: volumes 191–200

1999
*
Discrete Mathematics
*

Puech,

doi:10.1016/s0012-365x(99)90004-3
fatcat:xbhsnsjfxbcp7llwdhvprlpk6q
*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. ...##
###
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

doi:10.1016/s0012-365x(03)00333-9
fatcat:geqfygze3nef7fqfzbgxdoep6q
*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. ...##
###
An Alternative Method to Crossing Minimization on Hierarchical Graphs

2001
*
SIAM Journal on Optimization
*

A common method

doi:10.1137/s1052623498334013
fatcat:7qbe5ufra5a3jcepeqgdgggelm
*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 ). ...##
###
Master index of volumes 161–170

1997
*
Discrete Mathematics
*

Ryjacek,

doi:10.1016/s0012-365x(97)80759-5
fatcat:gk2zgbbx5nbnzbtsvdvo2mkqbi
*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 ...##
###
An alternative method to crossing minimization on hierarchical graphs
[chapter]

1997
*
Lecture Notes in Computer Science
*

A common method

doi:10.1007/3-540-62495-3_57
fatcat:e45bozof6jfznpnhz7petptn6m
*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. ...##
###
Master index of volumes 121–130

1994
*
Discrete Mathematics
*

Whitehead, A characterization

doi:10.1016/0012-365x(94)90081-7
fatcat:5c53tthgpjd5fclhixgi3c4bnm
*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. ...##
###
Master index to volumes 251-260

2003
*
Discrete Mathematics
*

Pfender, Pancyclicity in

doi:10.1016/s0012-365x(02)00784-7
fatcat:2c4y6lmnybeuxcqr55ngld7r7e
*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. ...##
###
FPT Algorithms for Finding Near-Cliques in c-Closed Graphs
[article]

2021
*
arXiv
*
pre-print

In this work, we prove that many different kinds

arXiv:2007.09768v4
fatcat:z6eu4ca7orez5cdiexwavuzgg4
*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 ...##
###
Subject Index Volumes 1–200

2001
*
Discrete Mathematics
*

freedom, 4060

doi:10.1016/s0012-365x(00)00471-4
fatcat:znxg54q6ifgutnhzj3urcw455y
*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, ...##
###
Local search in coding theory

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. ...

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