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## Filters

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Extremal connected graphs for independent domination number

2004
*
Discrete Mathematics
*

For certain situations, one

doi:10.1016/j.disc.2003.06.011
fatcat:kg6cot6iareonit6pzfhm3dy7q
*of*which occurs when n is*a*perfect square,*the**extremal**graphs*have*a*particularly simple structure. ...*A*general characterization*of*connected*graphs*on n vertices having*the*maximum possible independent domination number*of*n + 2 − 2 √ n is given. ... Most*extremal**graphs*do not satisfy*conditions*(*a*) -(d)*of*Lemma 19. We immediately obtain*a*structural characterization*of*these*graphs*. ...##
###
Overlapping of functions

1997
*
Mathematical Notes
*

*The*definition

*of*an

*extreme*ray

*of*

*a*

*set*

*A*is similar. ... L -L and for any

*extreme*point -2

*of*

*the*

*set*epi f** fl L -L

*the*

*graph*

*of*

*the*function contains an enveloping subset

*of*-~ + L. ...

##
###
Extremal Regular Graphs: Independent Sets and Graph Homomorphisms

2017
*
The American mathematical monthly
*

This survey concerns regular

doi:10.4169/amer.math.monthly.124.9.827
fatcat:yitbj67qlzcf5enqy2r5k3bw2y
*graphs*that are*extremal*with respect to*the*number*of*independent*sets*, and more generally,*graph*homomorphisms. ... More precisely, in*the*family*of**of*d-regular*graphs*, which*graph*G maximizes/minimizes*the*quantity i(G)^1/v(G),*the*number*of*independent*sets*in G normalized exponentially by*the*size*of*G? ... Independent*Sets*Let G = (V , E) be*a**graph*. An independent*set*is*a*subset*of**the*vertices with no two adjacent. Question. ...##
###
Extremal graph problems with symmetrical extremal graphs. Additional chromatic conditions

1974
*
Discrete Mathematics
*

*The*main result

*of*this paper is that for

*a*special, but rather wide class

*of*"sample

*graphs*",

*the*

*extremal*

*graphs*, i.e,

*the*

*graphs*

*of*n vertices without subgraphs isomorphic to

*the*sample

*graph*and having ... This result remains valid even in

*the*case when

*the*'

*condition*"

*the*

*graph*does not contain

*the*sample

*graph*" is replaced by

*the*

*condition*"

*the*

*graph*does not contain

*the*sample

*graph*and its chromatic ... We do not distinguish between

*a*chromatic

*condition*and

*the*family

*of*

*graphs*, satisfying this

*condition*. (1) Let

*A*be

*the*family

*of*at least r-chromatic

*graphs*. Then

*A*is

*a*chromatic

*condition*. ...

##
###
Extremal graph problems with symmetrical extremal graphs. Additional chromatic conditions

1974
*
Discrete Mathematics
*

*The*main result

*of*this paper is that for

*a*special, but rather wide class

*of*"sample

*graphs*",

*the*

*extremal*

*graphs*, i.e,

*the*

*graphs*

*of*n vertices without subgraphs isomorphic to

*the*sample

*graph*and having ... This result remains valid even in

*the*case when

*the*'

*condition*"

*the*

*graph*does not contain

*the*sample

*graph*" is replaced by

*the*

*condition*"

*the*

*graph*does not contain

*the*sample

*graph*and its chromatic ... We do not distinguish between

*a*chromatic

*condition*and

*the*family

*of*

*graphs*, satisfying this

*condition*. (1) Let

*A*be

*the*family

*of*at least r-chromatic

*graphs*. Then

*A*is

*a*chromatic

*condition*. ...

##
###
(c-)AND: A new graph model
[article]

2013
*
arXiv
*
pre-print

In this document, we study

arXiv:1306.1957v3
fatcat:dg35vicf2vg4pg2mhiv3bak2ia
*the*scope*of**the*following*graph*model: each vertex is assigned to*a*box in*a*metric space and to*a*representative element that belongs to that box. ... We give both,*a*combinatorial and an intersection characterization*of**the*model. ... Acknowledgements*The*authors would like to thank Antonio Fernández Anta and Marcos Kiwi because they are strongly involved in*the*origins*of*this study, even more, they contributed with enlightening talks ...##
###
Page 1527 of Automation and Remote Control Vol. 55, Issue 10
[page]

1994
*
Automation and Remote Control
*

*of*

*extreme*working regimes for

*a*particular manufacturing complex in

*the*form

*of*

*a*directed

*graph*G(Q, W), where

*the*

*set*Q

*of*vertices

*of*

*the*

*graph*corresponds to initial situations, objective situations ... to

*the*operations ut) € T(“+)) and fu) € T() are taken to coincide with

*the*

*sets*p (ut) and p()

*of*input

*conditions*

*of*these operations and have

*the*following forms: Piet!) ...

##
###
The decycling number of outerplanar graphs

2012
*
Journal of combinatorial optimization
*

In this paper, we provide

doi:10.1007/s10878-012-9455-1
fatcat:ehm3ddmy3bebvfhdzlsdmmcvwu
*a*necessary and sufficient*condition*for an outerplanar*graph*being upper-*extremal*. ... On*the*other hand, we find*a*class S*of*outerplanar*graphs*none*of*which is lower-*extremal*and show that if G has no subdivision*of*S for all S ∈ S, then G is lower-*extremal*. ... On*the*other hand, we provide*a*sufficient*condition*for an outerplanar*graph*being lower-*extremal*. ...##
###
Maximizing the number of maximal independent sets of a fixed size
[article]

2020
*
arXiv
*
pre-print

Muller, determined

arXiv:2012.06066v2
fatcat:645h4x5yyfdyfeoktdpwc2xjju
*the*maximum number*of*maximal independent*sets*in*a**graph*on n vertices, as well as*the**extremal**graphs*. ... In this paper we maximize*the*number*of*maximal independent*sets**of**a*fixed size for all*graphs**of*order n and determine*the**extremal**graphs*. Our result generalizes*the*classical result. ...*The*above*extremal*value is achieved if and only if*the*following*conditions*are simultaneously met. i). G − v is*a*t-cliques*extremal**graph**of*order n − 1. ...##
###
On Ramsey—Turán type theorems for hypergraphs

1982
*
Combinatorica
*

*condition*which decreases

*the*size

*of*

*the*maximal independent

*set*in G,, then

*the*number

*of*edges

*of*

*the*corresponding

*extremal*

*graphs*gets drastically reduced. ... E.g. for K; (and for

*a*more general class

*of*

*graphs*)

*the*

*condition*that

*the*largest independent

*set*has size o(n) does not change

*the*situation. We prove Remark. ...

##
###
On some interconnections between combinatorial optimization and extremal graph theory

2004
*
Yugoslav Journal of Operations Research
*

*The*uniting feature

*of*combinatorial optimization and

*extremal*

*graph*theory is that in both areas one should find extrema

*of*

*a*function defined in most cases on

*a*finite

*set*. ... While in combinatorial optimization

*the*point is in developing efficient algorithms and heuristics for solving specified types

*of*problems,

*the*

*extremal*

*graph*theory deals with finding bounds for various ... An instance is

*a*

*set*

*of*

*graphs*specified by

*the*number

*of*vertices and by other

*graph*invariants, i.e.

*the*

*set*

*of*instances is

*a*

*set*

*of*

*sets*

*of*

*graphs*. ...

##
###
A Generalization of Nemhauser and Trotter's Local Optimization Theorem
[article]

2009
*
arXiv
*
pre-print

We also outline an application

arXiv:0902.2149v1
fatcat:ufz3defh6fa73pgwm3eo5fp33m
*of*our*extremal*combinatorial approach to*the*problem*of*packing stars with*a*bounded number*of*leaves. ... Our generalization*of**the*Nemhauser-Trotter theorem implies that Bounded-Degree Deletion has*a*problem kernel with*a*linear number*of*vertices for every constant d. ...*A*packing P*of**a**graph*G is*a**set**of*pairwise vertex-disjoint subgraphs*of*G.*A**graph*has maximum degree d when every vertex in*the**graph*has degree at most d. ...##
###
Page 1157 of Automation and Remote Control Vol. 54, Issue 7
[page]

1993
*
Automation and Remote Control
*

Thus, applying

*the*dominant rule*of*choice to*graphs**of**a*non-strict partial ordering for all X C*A*coincides with*extrem*- ization choice according to*a*certain*set**of*criteria (Pareto rule), while choice ... for*graphs**of*non-strict weak ordering coincides with*the*conventional*extremization*choice according to*a*certain criterion. ...##
###
On extreme infinite doubly stochastic matrices

1987
*
Illinois Journal of Mathematics
*

*The*

*set*

*of*all

*extreme*points

*of*(, g) coincides with

*the*

*set*

*of*all exposed points

*of*( , ). Proof that F.ia by Obviously each exposed point is

*extreme*. Now let

*a*> 0 be such 1. ... We say that

*the*connected component H

*of*

*the*

*graph*G(P) is an

*extreme*tree if H is

*a*tree satisfying

*the*following

*conditions*: (,) H has no e-bitree. (, ,) H has at most one node corresponding to

*a*row ...

##
###
Page 1014 of American Mathematical Society. Proceedings of the American Mathematical Society Vol. 7, Issue 6
[page]

1956
*
American Mathematical Society. Proceedings of the American Mathematical Society
*

More precisely: let P be

*the**set**of*vertices*of**a*connected linear*graph*y and S*a*given*set**of*objects*of**the*same cardinality as P. ... Consider*a*connected linear*graph*y and*a*function F,(x1, x2, - - - ) where x; is*a*variable associated to*the*point P;*of**the**graph*. Let 42%2 +--+ 2a;2--- be*a*given*set**of*numbers. ...
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