Results 41 to 50 of about 1,119 (103)
Avoiding rainbow 2-connected subgraphs
Open Mathematics, 2017 While defining the anti-Ramsey number Erdős, Simonovits and Sós mentioned that the extremal colorings may not be unique. In the paper we discuss the uniqueness of the colorings, generalize the idea of their construction and show how to use it to ...
Gorgol Izolda
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More on the Rainbow Disconnection in Graphs
Discussiones Mathematicae Graph Theory, 2022 Let G be a nontrivial edge-colored connected graph. An edge-cut R of G is called a rainbow-cut if no two of its edges are colored the same. An edge-colored graph G is rainbow disconnected if for every two vertices u and v of G, there exists a u-v-rainbow-
Bai Xuqing +3 more
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Rainbow spanning structures in graph and hypergraph systems
Forum of Mathematics, Sigma, 2023 We study the following rainbow version of subgraph containment problems in a family of (hyper)graphs, which generalizes the classical subgraph containment problems in a single host graph. For a collection $\mathit {\mathbf {G}}=\{G_1, G_2,\ldots , G_{
Yangyang Cheng +3 more
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Note on minimally $k$-rainbow connected graphs [PDF]
, 2012 An edge-colored graph $G$, where adjacent edges may have the same color, is {\it rainbow connected} if every two vertices of $G$ are connected by a path whose edge has distinct colors.
Li, Hengzhe +3 more
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Discussiones Mathematicae Graph Theory, 2018 A total-colored graph G is rainbow total-connected if any two vertices of G are connected by a path whose edges and internal vertices have distinct colors.
Sun Yuefang, Jin Zemin, Tu Jianhua
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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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A Tur\'an-type problem on degree sequence [PDF]
, 2013 Given $p\geq 0$ and a graph $G$ whose degree sequence is $d_1,d_2,\ldots,d_n$, let $e_p(G)=\sum_{i=1}^n d_i^p$. Caro and Yuster introduced a Tur\'an-type problem for $e_p(G)$: given $p\geq 0$, how large can $e_p(G)$ be if $G$ has no subgraph of a ...
Li, Xueliang, Shi, Yongtang
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On the cycle structure of hamiltonian k-regular bipartite graphs of order 4k [PDF]
, 2009 It is shown that a hamiltonian $n/2$-regular bipartite graph $G$ of order $2n>8$ contains a cycle of length $2n-2$. Moreover, if such a cycle can be chosen to omit a pair of adjacent vertices, then $G$ is bipancyclic.Comment: 3 ...
Adamus, Janusz
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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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A note on blockers in posets [PDF]
, 2004 The blocker $A^{*}$ of an antichain $A$ in a finite poset $P$ is the set of elements minimal with the property of having with each member of $A$ a common predecessor. The following is done: 1.
Björner, Anders, Hultman, Axel
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