Results 21 to 30 of about 21,321 (296)
Vertex degrees and 2-cuts in graphs with many hamiltonian vertex-deleted subgraphs [PDF]
, 2022 A 2-connected non-hamiltonian graph G is a k-graph if for exactly k < |V(G)| vertices in G, removing such a vertex yields a non-hamiltonian graph. We characterise k-graphs of connectivity 2 and describe structurally interesting examples of such graphs ...
Zamfirescu, Carol
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On the Vertex-Degree Based Invariants of Digraphs
Discrete Mathematics Letters, 2021 Let $D=(V,A)$ be a digraphs without isolated vertices. A vertex-degree based invariant $I(D)$ related to a real function $φ$ of $D$ is defined as a summation over all arcs, $I(D) = \frac{1}{2}\sum_{uv\in A}{φ(d_u^+,d_v^-)}$, where $d_u^+$ (resp. $d_u^-$) denotes the out-degree (resp. in-degree) of a vertex $u$.
Hanyuan Deng +4 more
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Fringe trees for random trees with given vertex degrees [PDF]
, 2023 We prove asymptotic normality for the number of fringe subtrees isomorphic to any given tree in uniformly random trees with given vertex degrees. As applications, we also prove corresponding results for random labelled trees with given vertex degrees ...
Holmgren, Cecilia +2 more
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Degree distance and vertex-connectivity
Discrete Applied Mathematics, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Patrick Ali +2 more
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Random graphs with given vertex degrees and switchings [PDF]
, 2020 Random graphs with a given degree sequence are often constructed using the configuration model, which yields a random multigraph. We may adjust this multigraph by a sequence of switchings, eventually yielding a simple graph.
Janson, Svante,, Svante Janson
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Fringe Trees for Random Trees With Given Vertex Degrees [PDF]
We prove asymptotic normality for the number of fringe subtrees isomorphic to any given tree in uniformly random trees with given vertex degrees. As applications, we also prove corresponding results for random labeled trees with given vertex degrees, for
Berzunza Ojeda, Gabriel +5 more
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Crossing number is hard for cubic graphs [PDF]
, 2004 It was proved by [Garey, Johnson] that computing the crossing number of a graph is an NP -hard problem. Their reduction, however, used parallel edges and vertices of very high degrees.
Petr Hlineny +7 more
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Vertex arboricity and maximum degree
Discrete Mathematics, 1995 This paper mainly proves that if a connected graph \(G= (V,E)\) is neither a cycle nor a clique, then there is a coloring of \(V\) with at most \(\lceil {{\Delta (G)} \over 2} \rceil\) colors such that all color classes induce forests and one of them is a minimum induced forest in \(G\).
Paul A. Catlin, Hong-Jian Lai
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Dually vertex-oblique graphs [PDF]
, 2007 A vertex with neighbours of degrees d1⩾⋯⩾dr has vertex type (d1,…,dr). A graph is vertex-oblique if each vertex has a distinct vertex type (no graph can have distinct degrees). Schreyer et al.
Alastair Farrugia, Farrugia, Alastair
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On Triangulations with High Vertex Degree [PDF]
Annals of Combinatorics, 2008 We solve three enumerative problems concerning families of planar maps. More precisely, we establish algebraic equations for the generating function of non-separable triangulations in which all vertices have degree at least d, for a certain value d chosen in {3, 4, 5}.
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