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Extremal connected graphs for independent domination number
2004
Discrete Mathematics
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For certain situations, one 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. ...
doi:10.1016/j.disc.2003.06.011
fatcat:kg6cot6iareonit6pzfhm3dy7q
Overlapping of functions
1997
Mathematical Notes
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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. ...
doi:10.1007/bf02354996
fatcat:otw6znnqobarnph5itk2jtgkyu
Extremal Regular Graphs: Independent Sets and Graph Homomorphisms
2017
The American mathematical monthly
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This survey concerns regular 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. ...
doi:10.4169/amer.math.monthly.124.9.827
fatcat:yitbj67qlzcf5enqy2r5k3bw2y
Extremal graph problems with symmetrical extremal graphs. Additional chromatic conditions
1974
Discrete Mathematics
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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. ...
doi:10.1016/s0012-365x(74)80010-5
fatcat:zcpoxuttgbarroke5qe72gduyu
Extremal graph problems with symmetrical extremal graphs. Additional chromatic conditions
1974
Discrete Mathematics
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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. ...
doi:10.1016/0012-365x(74)90044-2
fatcat:xkadun3bo5awzcjq72y63wqysu
(c-)AND: A new graph model
[article]
2013
arXiv
pre-print
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In this document, we study 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 ...
arXiv:1306.1957v3
fatcat:dg35vicf2vg4pg2mhiv3bak2ia
Page 1527 of Automation and Remote Control Vol. 55, Issue 10
[page]
1994
Automation and Remote Control
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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
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In this paper, we provide 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. ...
doi:10.1007/s10878-012-9455-1
fatcat:ehm3ddmy3bebvfhdzlsdmmcvwu
Maximizing the number of maximal independent sets of a fixed size
[article]
2020
arXiv
pre-print
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Muller, determined 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. ...
arXiv:2012.06066v2
fatcat:645h4x5yyfdyfeoktdpwc2xjju
On Ramsey—Turán type theorems for hypergraphs
1982
Combinatorica
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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. ...
doi:10.1007/bf02579235
fatcat:fze64hkmifdxziedtofdbmeqgy
On some interconnections between combinatorial optimization and extremal graph theory
2004
Yugoslav Journal of Operations Research
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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. ...
doi:10.2298/yjor0402147c
fatcat:ayreclwmgje6ph7tu6upzvrbtq
A Generalization of Nemhauser and Trotter's Local Optimization Theorem
[article]
2009
arXiv
pre-print
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We also outline an application 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. ...
arXiv:0902.2149v1
fatcat:ufz3defh6fa73pgwm3eo5fp33m
Page 1157 of Automation and Remote Control Vol. 54, Issue 7
[page]
1993
Automation and Remote Control
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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
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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 ...
doi:10.1215/ijm/1256063569
fatcat:wjqqimg5ibajpedan7tufgai3i
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
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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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