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...Continuing to provide a carefully written, thorough introduction, Graphs & Digraphs, Fifth Edition expertly describes the concepts, theorems, history, and...

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Graphs & digraphs
3. ed., 1. CRC Press repr.

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by Ferrero, Daniela   Lesniak, Linda Published in Graphs and combinatorics (01.11.2018)
...We prove that for any integers p k 3<![CDATA[ ]]>pa[yen]ka[yen]3<![CDATA[ ]]> and any k-tuple of positive integers (n.sub.1, ,n.sub.k)<![CDATA[...
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...In 1972 Chvátal gave a well-known sufficient condition for a graphical sequence to be forcibly Hamiltonian, and showed that in some sense his condition is best...

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...Graphs & Digraphs masterfully employs student-friendly exposition, clear proofs, abundant examples, and numerous exercises to provide an essential...
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by Dudek, Andrzej   Lesniak, Linda Published in Discrete mathematics (06.06.2016)
...In this paper, we study an analogue of size-Ramsey numbers for vertex colorings. For a given number of colors  r and a graph  G the vertex size-Ramsey number...
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...Let c, m, n be integers with n⩾c⩾3, and let G be a graph of order n with m edges. A classical theorem by Erdős and Gallai states that if m>(c−1)(n−1)/2, then G...
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...Let c, m, n be integers with n[greater than or equal to]c[greater than or equal to]3, and let G be a graph of order n with m edges. A classical theorem by...
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...Given positive integers k≤m≤n, a graph G of order n is (k,m)-pancyclic if for any set of k vertices of G and any integer r with m≤r≤n, there is a cycle of...

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...Given positive integers k ≤ m ≤ n, a graph G of order n is (k, m)-pancyclic ordered if for any set of k vertices of G and any integer r with m ≤ r ≤ n, there...

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...The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor...
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Published in Discrete mathematics (06.07.2016)
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...Let G be a graph of order n and circumference c ( G ) . Let G ¯ be the complement of G . We prove that max { c ( G ) , c ( G ¯ ) } ≥ ⌈ 2 n 3 ⌉ and show...

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...The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor...
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by Ferrero, Daniela   Lesniak, Linda
23.01.2018
...We prove that for any integers $p\geq k\geq 3$ and any $k$-tuple of positive integers $(n_1,\ldots ,n_k)$ such that $p=\sum _{i=1}^k{n_i}$ and \$n_1\geq n_2\geq...

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...Gary Chartrand has influenced the world of Graph Theory for almost half a century. He has supervised more than a score of Ph.D. dissertations and written...
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by Lesniak, Linda   White, Arthur T
01.11.2017
...We show, with simple combinatorics, that if the dimples on a golf ball are all 5-sided and 6-sided polygons, with three dimples at each “vertex”, then no...