Results 31 to 40 of about 10,864 (212)
On hamiltonicity of 1-tough triangle-free graphs
Electronic Journal of Graph Theory and Applications, 2021 Let ω(G) denote the number of components of a graph G. A connected graph G is said to be 1-tough if ω(G − X)≤|X| for all X ⊆ V(G) with ω(G − X)>1. It is well-known that every hamiltonian graph is 1-tough, but that the reverse statement is not true in ...
Wei Zheng, Hajo Broersma, Ligong Wang
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Intersection Dimension and Graph Invariants
Discussiones Mathematicae Graph Theory, 2021 We show that the intersection dimension of graphs with respect to several hereditary properties can be bounded as a function of the maximum degree. As an interesting special case, we show that the circular dimension of a graph with maximum degree Δ is at
Aravind N.R., Subramanian C.R.
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Evasiveness and the Distribution of Prime Numbers [PDF]
, 2010 We confirm the eventual evasiveness of several classes of monotone graph properties under widely accepted number theoretic hypotheses. In particular we show that Chowla's conjecture on Dirichlet primes implies that (a) for any graph $H$, "forbidden ...
Babai, Laszlo +3 more
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Well-quasi-ordering versus clique-width : new results on bigenic classes. [PDF]
, 2016 Daligault, Rao and Thomassé conjectured that if a hereditary class of graphs is well-quasi-ordered by the induced subgraph relation then it has bounded clique-width.
A Atminas +21 more
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Forbidden subgraphs in connected graphs
Theoretical Computer Science, 2004 Given a set $ =\{H_1,H_2,...\}$ of connected non acyclic graphs, a $ $-free graph is one which does not contain any member of $% $ as copy. Define the excess of a graph as the difference between its number of edges and its number of vertices. Let ${\gr{W}}_{k, }$ be theexponential generating function (EGF for brief) of connected $ $-free graphs ...
Ravelomanana, Vlady, Loÿs, Thimonier
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Hereditary Equality of Domination and Exponential Domination in Subcubic Graphs
Discussiones Mathematicae Graph Theory, 2021 Let γ(G) and γe(G) denote the domination number and exponential domination number of graph G, respectively. Henning et al., in [Hereditary equality of domination and exponential domination, Discuss. Math. Graph Theory 38 (2018) 275–285] gave a conjecture:
Chen Xue-Gang, Wang Yu-Feng, Wu Xiao-Fei
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Electronic Journal of Graph Theory and Applications, 2018 We find the structure of graphs that have no C4, $\overline{C}_4$, C5, S3, chair and co-chair as induced subgraphs. Then we deduce the structure of the graphs having no induced C4, $\overline{C_4}$, S3, chair and co-chair and the structure of the graphs ...
Salman Ghazal
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Forbidden subgraphs for chorded pancyclicity
Discrete Mathematics, 2017 We call a graph $G$ pancyclic if it contains at least one cycle of every possible length $m$, for $3\le m\le |V(G)|$. In this paper, we define a new property called chorded pancyclicity. We explore forbidden subgraphs in claw-free graphs sufficient to imply that the graph contains at least one chorded cycle of every possible length $4, 5, \ldots, |V(G)|
Megan Cream +2 more
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Forbidden subgraphs, stability and hamiltonicity
Discrete Mathematics, 1999 AbstractWe study the stability of some classes of claw-free graphs defined in terms of forbidden subgraphs under the closure operation defined in [10]. We characterize all connected graphs A such that the class of all CA-free graphs (where C denotes the claw) is stable. Using this result, we prove that every 2-connected and CHP8-free, CHZ5-free or CHN1,
Jan Brousek +2 more
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On edge-sets of bicliques in graphs [PDF]
, 2012 A biclique is a maximal induced complete bipartite subgraph of a graph. We investigate the intersection structure of edge-sets of bicliques in a graph. Specifically, we study the associated edge-biclique hypergraph whose hyperedges are precisely the edge-
Groshaus, Marina +2 more
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