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The structure of imperfect critically strongly-imperfect graphs

Elefterie Olaru
<span title="">1996</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
The family of all critically strongly-imperfect graphs decomposes in two nonempty classes: perfect and imperfect ones.  ...  In this paper we characterize the critically strongly-imperfect graphs which are, simultaneously, imperfect. We prove that these are precisely the holes of odd length ~> 5 or their complements.  ...  The problem is: how to characterize, in a simple way, the structure of critically s-imperfect (c-imperfect) graphs?  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0012-365x(95)00058-5">doi:10.1016/0012-365x(95)00058-5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xnswyv5pszbzxjkwhcvjdrd22m">fatcat:xnswyv5pszbzxjkwhcvjdrd22m</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190325163950/https://core.ac.uk/download/pdf/82077925.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/7c/82/7c82557ef63d5aa70536158be422953d4be686ca.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0012-365x(95)00058-5"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

New Results on Minimal Strongly Imperfect Graphs

V. Anastasoaei, E. Olaru
<span title="">2008</span> <i title="Alexandru Ioan Cuza University of Iasi"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/drxmw4lrtff4fptvxxstnpfww4" style="color: black;">Scientific Annals of Computer Science</a> </i> &nbsp;
Thus we introduce the notion of critical (co-critical) pair of vertices, and we prove that any vertex of a minimal s-imperfect (minimal c-imperfect) graph is contained in a critical (co-critical) pair,  ...  Also, we characterize the triangle-free minimal s-imperfect graphs. (By s-perfect we mean the complement of a strongly perfect graph.)  ...  Acknowledgments The authors would like to thank the referees for their constructive comments that led to a much improved presentation of the paper.  ... 
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Grade 12 Learners' Perceptions of Opportunities to Learn Imperfect Market Structures: Frances Baard District

Wellington Itai Manzi, Moeketsi Mosia, Boitumelo Moreeng, Thomas Masvosve
<span title="2021-09-30">2021</span> <i title="Society for Research and Knowledge Management"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fflscqgz4zdo5mqk5mfvalkrlq" style="color: black;">International Journal of Learning, Teaching and Educational Research</a> </i> &nbsp;
This empirical study sought to investigate the grade 12 economics learners' perceptions of opportunities to learn imperfect market structures in selected schools in the Francis Baard District of Northern  ...  Overall, the study showed that little or no opportunities to learn were being created for learners to master the concept of imperfect market structures.  ...  in the study of imperfect market structures.  ... 
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Critical and Anticritical Edges in Perfect Graphs [chapter]

Annegret Wagler
<span title="">2001</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We call an edge e of a perfect graph G critical if G − e is imperfect and say further that e is anticritical with respect to the complementary graph G.  ...  Finally, we study whether we can order the edges of certain perfect graphs such that deleting all the edges yields a sequence of perfect graphs ending up with a stable set.  ...  In order to verify or falsify the Strong Perfect Graph Conjecture, many structural properties of minimally imperfect graphs have been discovered.  ... 
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Page 1447 of Mathematical Reviews Vol. , Issue 97C [page]

<span title="">1997</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Ioan Tomescu (Bucharest) 97¢:05065 05C15 Olaru, Elefterie (R-GALA; Galati) The structure of imperfect critically strongly-imperfect graphs.  ...  In this paper we characterize the critically strongly-imperfect graphs which are, simultaneously, imperfect.  ... 
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Author index to volume 156 (1996)

<span title="">1996</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
Jimbo, A series of identities for the coefficients of inverse matrices on a Hamming scheme (Note) H., Hamiltonian circuits in chordal bipartite graphs (Note) E., The structure of imperfect critically strongly-imperfect  ...  Gross, A tight lower bound on the maximum genus of a simplicial graph (1 3) 83-102 Cohn, J.H.E., Complex D-optimal designs (1-3) 237-241 Curran, S.J. and J.A.  ... 
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New classes of critical kernel-imperfect digraphs

Hortensia Galeana-Sánchez, Victor Neumann-Lara
<span title="">1998</span> <i title="Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Gora"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/g64zvtslcjdqncvrfbmvf422qi" style="color: black;">Discussiones Mathematicae Graph Theory</a> </i> &nbsp;
The aim of the paper is to construct critical kernelimperfect digraphs of a special structure, a general method is developed which permits to build critical kernel-imperfect-digraphs whose asymmetrical  ...  Although many classes of critical kernel-imperfect-digraphs have been constructed, all of them are digraphs such that the block-cutpoint tree of its asymmetrical part is a path.  ...  If the complement of the graph G is strongly perfect, then G is solvable.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.7151/dmgt.1065">doi:10.7151/dmgt.1065</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bqyienspgnb4bdz57ti2qo4cpe">fatcat:bqyienspgnb4bdz57ti2qo4cpe</a> </span>
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Recent Problems and Results about Kernels in Directed Graphs [chapter]

C. Berge, P. Duchet
<span title="">1991</span> <i title="Elsevier"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/e6ft7vn5prcbflhmcmkbrfkjfa" style="color: black;">Annals of Discrete Mathematics</a> </i> &nbsp;
In Section 1, we survey the existence theorems for a kernel; in Section 2, we discuss a new conjecture which could constitute a bridge between the kernel problems and the perfect graph conjecture.  ...  In fact, we believe that a graph is 'quasi-perfect' if and only if it is perfect.  ...  A critical kernel-imperfect graph is a graph G without kernel such that every strict subgraph is kernel-perfect. We have: Proposition 1.2. A critical kernel-imperfect graph is strongly connected.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0167-5060(08)71035-5">doi:10.1016/s0167-5060(08)71035-5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qfkrtrs2rncn7p3mcmmh2bppr4">fatcat:qfkrtrs2rncn7p3mcmmh2bppr4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20100625061942/http://www-math.ucdenver.edu/~mferrara/seminar/Berge_Duchet.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a0/4a/a04a28e9e5d65ac4cfda500946555202e85604a0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0167-5060(08)71035-5"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Recent problems and results about kernels in directed graphs

C. Berge, P. Duchet
<span title="">1990</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
In Section 1, we survey the existence theorems for a kernel; in Section 2, we discuss a new conjecture which could constitute a bridge between the kernel problems and the perfect graph conjecture.  ...  In fact, we believe that a graph is 'quasi-perfect' if and only if it is perfect.  ...  A critical kernel-imperfect graph is a graph G without kernel such that every strict subgraph is kernel-perfect. We have: Proposition 1.2. A critical kernel-imperfect graph is strongly connected.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0012-365x(90)90346-j">doi:10.1016/0012-365x(90)90346-j</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3isksiio4jfo7nr5foo25xbqdu">fatcat:3isksiio4jfo7nr5foo25xbqdu</a> </span>
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Page 4009 of Mathematical Reviews Vol. , Issue 83j [page]

<span title="">1983</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
This inequality can be used either to obtain bounds for certain Ramsey numbers from the parameters of known strongly regular graphs, or to show the nonexistence of certain strongly regular graphs from  ...  This paper relates the Ramsey numbers r(B,,,B,) to the existence of strongly regular graphs. (Here B,, is the “book” graph of n triangles sharing a common edge.)  ... 
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The Strong Perfect Graph Conjecture: 40 years of attempts, and its resolution

F. Roussel, I. Rusu, H. Thuillier
<span title="">2009</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
" approaches whose aim was to get more information about the properties and structure of perfect graphs, without a direct impact on the SPGC.  ...  This paper is an unbalanced survey of the attempts to solve the SPGC; unbalanced, because (1) we devote a significant part of it to the 'primitive graphs and structural faults' paradigm which led to the  ...  Acknowledgements The authors wish to strongly acknowledge J.-L.  ... 
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Imperfection sensitivity of column instability revisited

Ana M. Girão Coelho, Pedro D. Simão, M. Ahmer Wadee
<span title="">2013</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2etcd5lr4vdyllxszqofpuyray" style="color: black;">Journal of constructional steel research</a> </i> &nbsp;
The buckling of columns is the classic problem in structural stability.  ...  For modelling purposes, geometrical, material and structural imperfections are usually considered by means of an equivalent initial geometric imperfection, in the form of an initial curvature or out-of-straightness  ...  Table 1 shows the calculated values of the ratio of the strength of the imperfect structure to that of the perfect structure (N max /N cr ).  ... 
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Page 5119 of Mathematical Reviews Vol. , Issue 95i [page]

<span title="">1995</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
(MEX-NAM-IM; México City) New extensions of kernel perfect digraphs to kernel imperfect critical digraphs. (English summary) Graphs Combin. 10 (1994), no. 4, 329-336.  ...  A general method is developed to extend a kernel-perfect directed graph to a critical kernel-imperfect directed graph. B. Zelinka (Liberec) 95i:05065 05C20 05C75 Harju, T.  ... 
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Experimental and Theoretical Design Methodology of Hemispherical Shells under Extreme Static Loading

Sh. U. Galiev, J. Blachut, E. D. Skurlatov, O. P. Panova, G. Moltschaniwskyj, Z. Cui
<span title="">2004</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ydbfaprlmzd5jdcrivjt3hqn44" style="color: black;">Strength of Materials</a> </i> &nbsp;
Set of graphs for designing of imperfect hemispheres filled with styrofoam. Coefficients of the nonlinear (cubic) regression equations were determined from experiments in 9 points of x 1 -x 2 plane.  ...  Using the regression equations and graphs depicted in Figs. 2-3 the different hemispherical elements o f structures could be designed with ease.  ... 
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Comparative Study Concerning the Methods of Calculation of the Critical Axial Buckling Load for Stiffened Cylindrical Shells

Maria Zaharia, Alexandru Pupazescu, Cristian Mihai Petre
<span title="2018-09-15">2018</span> <i title="Revista de Chimie SRL"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/eg4jwh4ncfdpde7ewcgpl74r7i" style="color: black;">Revista de Chimie</a> </i> &nbsp;
As demonstrated in numerous theoretical and experimental studies [1], the buckling behaviour of stiffened cylindrical shells (SCS) is strongly influenced by the presence of geometric imperfections caused  ...  of the critical buckling load.  ...  The graph in figure 3 indicates that the curves of variation of radial deviations have the same shape.  ... 
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