Results 61 to 70 of about 313,328 (262)
Sufficient conditions for maximally edge-connected and super-edge-connected graphs
Communications in Combinatorics and Optimization, 2017 Let $G$ be a connected graph with minimum degree $\delta$ and edge-connectivity $\lambda$. A graph is maximally edge-connected if $\lambda=\delta$, and it is super-edge-connected if every minimum edge-cut is trivial; that is, if every ...
Lutz Volkmann, Zhen-Mu Hong
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On Conditional Connectivity of the Cartesian Product of Cycles
Discussiones Mathematicae Graph Theory, 2023 The conditional h-vertex (h-edge) connectivity of a connected graph H of minimum degree k > h is the size of a smallest vertex (edge) set F of H such that H − F is a disconnected graph of minimum degree at least h. Let G be the Cartesian product of r ≥ 1
Saraf J.B., Borse Y.M., Mundhe Ganesh
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Vertices of degree k in edge-minimal, k-edge-connected graphs
, 2009 Halin showed that every edge minimal, k-vertex connected graph has a vertex of degree k. In this note, we prove the analogue to Halin's theorem for edge-minimal, k-edge-connected graphs. We show there are two vertices of degree k in every edge-minimal, k-edge-connected graph.
Kingsford, Carl, Marçais, Guillaume
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Overfullness of edge‐critical graphs with small minimal core degree
Journal of Graph Theory, 2023 AbstractLet be a simple graph. Let and be the maximum degree and the chromatic index of , respectively. We call overfull if , and critical if for every proper subgraph of . Clearly, if is overfull then . The core of , denoted by , is the subgraph of induced by all its maximum degree vertices.
Yan Cao +3 more
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FEBS Letters, EarlyView.This study reveals how the mitochondrial protein Slm35 is regulated in Saccharomyces cerevisiae. The authors identify stress‐responsive DNA elements and two upstream open reading frames (uORFs) in the 5′ untranslated region of SLM35. One uORF restricts translation, and its mutation increases Slm35 protein levels and mitophagy.
Hernán Romo‐Casanueva +5 more
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Forbidden Subgraphs for Collapsible Graphs and Supereulerian Graphs
Discussiones Mathematicae Graph Theory, 2022 In this paper, we completely characterize the connected forbidden subgraphs and pairs of connected forbidden subgraphs that force a 2-edge-connected (2-connected) graph to be collapsible.
Liu Xia, Xiong Liming
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In situ molecular organization and heterogeneity of the Legionella Dot/Icm T4SS
FEBS Letters, EarlyView.We present a nearly complete in situ model of the Legionella Dot/Icm type IV secretion system, revealing its central secretion channel and identifying new components. Using cryo‐electron tomography with AI‐based modeling, our work highlights the structure, variability, and mechanism of this complex nanomachine, advancing understanding of bacterial ...
Przemysław Dutka +11 more
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An Extension of Kotzig’s Theorem
Discussiones Mathematicae Graph Theory, 2016 In 1955, Kotzig proved that every 3-connected planar graph has an edge with the degree sum of its end vertices at most 13, which is tight. An edge uv is of type (i, j) if d(u) ≤ i and d(v) ≤ j.
Aksenov Valerii A. +2 more
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The maximum number of edges in a graph with fixed edge-degree
Discrete Mathematics, 1998 For \(t\geq 17\) and \(n\geq 2t+2\), let \(G\) be a graph with \(n\) vertices whose complement is connected, and such that for all non-adjacent vertices \(u,v\), there are at least \(t\) common neighbours. It is proved that \(| E(G)|\geq \lceil((2t+1)n- 2t^2- 3)/2\rceil\) for \(n\leq 3t-1\), and \(| E(G)|\geq (t+1)n- t^2- t-3\) for \(n\geq 3t ...
Faudree, R.J., Sheehan, J.
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Sequence determinants of RNA G‐quadruplex unfolding by Arg‐rich regions
FEBS Letters, EarlyView.We show that Arg‐rich peptides selectively unfold RNA G‐quadruplexes, but not RNA stem‐loops or DNA/RNA duplexes. This length‐dependent activity is inhibited by acidic residues and is conserved among SR and SR‐related proteins (SRSF1, SRSF3, SRSF9, U1‐70K, and U2AF1).
Naiduwadura Ivon Upekala De Silva +10 more
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