1,874 research outputs found

    THE ELECTRONIC JOURNAL OF COMBINATORICS (2014), DS1.14 References

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    and Computing 11. The results of 143 references depend on computer algorithms. The references are ordered alphabetically by the last name of the first author, and where multiple papers have the same first author they are ordered by the last name of the second author, etc. We preferred that all work by the same author be in consecutive positions. Unfortunately, this causes that some of the abbreviations are not in alphabetical order. For example, [BaRT] is earlier on the list than [BaLS]. We also wish to explain a possible confusion with respect to the order of parts and spelling of Chinese names. We put them without any abbreviations, often with the last name written first as is customary in original. Sometimes this is different from the citations in other sources. One can obtain all variations of writing any specific name by consulting the authors database of Mathematical Reviews a

    Some exact values on Ramsey numbers related to fans

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    For two given graphs FF and HH, the Ramsey number R(F,H)R(F,H) is the smallest integer NN such that any red-blue edge-coloring of the complete graph KNK_N contains a red FF or a blue HH. When F=HF=H, we simply write R2(H)R_2(H). For an positive integer nn, let K1,nK_{1,n} be a star with n+1n+1 vertices, FnF_n be a fan with 2n+12n+1 vertices consisting of nn triangles sharing one common vertex, and nK3nK_3 be a graph with 3n3n vertices obtained from the disjoint union of nn triangles. In 1975, Burr, Erd\H{o}s and Spencer \cite{B} proved that R2(nK3)=5nR_2(nK_3)=5n for n2n\ge2. However, determining the exact value of R2(Fn)R_2(F_n) is notoriously difficult. So far, only R2(F2)=9R_2(F_2)=9 has been proved. Notice that both FnF_n and nK3nK_3 contain nn triangles and V(Fn)<V(nK3)|V(F_n)|<|V(nK_3)| for all n2n\ge 2. Chen, Yu and Zhao (2021) speculated that R2(Fn)R2(nK3)=5nR_2(F_n)\le R_2(nK_3)=5n for nn sufficiently large. In this paper, we first prove that R(K1,n,Fn)=3nεR(K_{1,n},F_n)=3n-\varepsilon for n1n\ge1, where ε=0\varepsilon=0 if nn is odd and ε=1\varepsilon=1 if nn is even. Applying the exact values of R(K1,n,Fn)R(K_{1,n},F_n), we will confirm R2(Fn)5nR_2(F_n)\le 5n for n=3n=3 by showing that R2(F3)=14R_2(F_3)=14.Comment: 10 pages, 3 figure

    Small Ramsey Numbers

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    We present data which, to the best of our knowledge, includes all known nontrivial values and bounds for specific graph, hypergraph and multicolor Ramsey numbers, where the avoided graphs are complete or complete without one edge. Many results pertaining to other more studied cases are also presented. We give references to all cited bounds and values, as well as to previous similar compilations. We do not attempt complete coverage of asymptotic behavior of Ramsey numbers, but concentrate on their specific values

    Technology transfer: Transportation

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    The application of NASA derived technology in solving problems related to highways, railroads, and other rapid systems is described. Additional areas/are identified where space technology may be utilized to meet requirements related to waterways, law enforcement agencies, and the trucking and recreational vehicle industries

    Advances in Discrete Applied Mathematics and Graph Theory

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    The present reprint contains twelve papers published in the Special Issue “Advances in Discrete Applied Mathematics and Graph Theory, 2021” of the MDPI Mathematics journal, which cover a wide range of topics connected to the theory and applications of Graph Theory and Discrete Applied Mathematics. The focus of the majority of papers is on recent advances in graph theory and applications in chemical graph theory. In particular, the topics studied include bipartite and multipartite Ramsey numbers, graph coloring and chromatic numbers, several varieties of domination (Double Roman, Quasi-Total Roman, Total 3-Roman) and two graph indices of interest in chemical graph theory (Sombor index, generalized ABC index), as well as hyperspaces of graphs and local inclusive distance vertex irregular graphs

    Graph Theory

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    Graph theory is a rapidly developing area of mathematics. Recent years have seen the development of deep theories, and the increasing importance of methods from other parts of mathematics. The workshop on Graph Theory brought together together a broad range of researchers to discuss some of the major new developments. There were three central themes, each of which has seen striking recent progress: the structure of graphs with forbidden subgraphs; graph minor theory; and applications of the entropy compression method. The workshop featured major talks on current work in these areas, as well as presentations of recent breakthroughs and connections to other areas. There was a particularly exciting selection of longer talks, including presentations on the structure of graphs with forbidden induced subgraphs, embedding simply connected 2-complexes in 3-space, and an announcement of the solution of the well-known Oberwolfach Problem

    The Connection, Summer 2009

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    Lindenwood University alumni magazine.https://digitalcommons.lindenwood.edu/the_connection/1027/thumbnail.jp
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