Results 61 to 70 of about 1,202 (110)
, 1997 Let S_m denote the m-vertex simple digraph formed by m-1 edges with a common tail. Let f(m) denote the minimum n such that every n-vertex tournament has a spanning subgraph consisting of n/m disjoint copies of S_m. We prove that m lg m - m lg lg m
Chen, Guantao +2 more
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Singular Turán Numbers and Worm-Colorings
Discussiones Mathematicae Graph Theory, 2022 A subgraph G of H is singular if the vertices of G either have the same degree in H or have pairwise distinct degrees in H. The largest number of edges of a graph on n vertices that does not contain a singular copy of G is denoted by TS(n, G).
Gerbner Dániel +3 more
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Path separation by short cycles
, 2016 Two Hamilton paths in $K_n$ are separated by a cycle of length $k$ if their union contains such a cycle. For small fixed values of $k$ we bound the asymptotics of the maximum cardinality of a family of Hamilton paths in $K_n$ such that any pair of paths ...
Cibulka +9 more
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Some results on the total proper k-connection number
Open Mathematics, 2022 In this paper, we first investigate the total proper connection number of a graph GG according to some constraints of G¯\overline{G}. Next, we investigate the total proper connection numbers of graph GG with large clique number ω(G)=n−s\omega \left(G)=n ...
Ma Yingbin, Zhang Hui
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Random algebraic construction of extremal graphs [PDF]
, 2015 In this expository paper, we present a motivated construction of large graphs not containing a given complete bipartite subgraph. The key insight is that the algebraic constructions yield very non-smooth probability distributions.Comment: 8 ...
Bukh, Boris
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A majorization method for localizing graph topological indices
, 2011 This paper presents a unified approach for localizing some relevant graph topological indices via majorization techniques. Through this method, old and new bounds are derived and numerical examples are provided, showing how former results in the ...
Alderson +34 more
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On the maximal Aa -index of graphs with a prescribed number of edges
Special MatricesFor any real number α∈[0,1]\alpha \in \left[\mathrm{0,1}], by the Aα{A}_{\alpha }-matrix of a graph GG, we mean the matrix Aα(G)=αD(G)+(1−α)A(G){A}_{\alpha }\left(G)=\alpha D\left(G)+\left(1-\alpha )A\left(G), where A(G)A\left(G) and D(G)D\left(G) are ...
Chang Ting-Chung, Tam Bit-Shun
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Bounds on F-index of tricyclic graphs with fixed pendant vertices
Open Mathematics, 2020 The F-index F(G) of a graph G is obtained by the sum of cubes of the degrees of all the vertices in G. It is defined in the same paper of 1972 where the first and second Zagreb indices are introduced to study the structure-dependency of total π-electron ...
Akram Sana +2 more
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Maximum Edge-Colorings Of Graphs
Discussiones Mathematicae Graph Theory, 2016 An r-maximum k-edge-coloring of G is a k-edge-coloring of G having a property that for every vertex v of degree dG(v) = d, d ≥ r, the maximum color, that is present at vertex v, occurs at v exactly r times. The r-maximum index χr′(G)$\chi _r^\prime (G)$
Jendrol’ Stanislav +1 more
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Minimally Strong Subgraph (k,ℓ)-Arc-Connected Digraphs
Discussiones Mathematicae Graph Theory, 2022 Let D = (V,A) be a digraph of order n, S a subset of V of size k and 2 ≤ k ≤ n. A subdigraph H of D is called an S-strong subgraph if H is strong and S ⊆ V (H). Two S-strong subgraphs D1 and D2 are said to be arc-disjoint if A(D1) ∩ A(D2) = ∅.
Sun Yuefang, Jin Zemin
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