Results 71 to 80 of about 2,876,957 (249)
Theory and Applications of Graphs, 2020 In his classical paper [14], Rosa introduced a hierarchical series of labelings called ρ, σ, β and α labeling as a tool to settle Ringel’s Conjecture which states that if T is any tree with m edges then the complete graph K2m+1 can be decomposed into 2m + 1 copies of T .
Sethuraman, G., Sujasree, M.
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Higher matching complexes of complete graphs and complete bipartite graphs [PDF]
Discrete Mathematics, 2022 For $r\geq 1$, the $r$-matching complex of a graph $G$, denoted $M_r(G)$, is a simplicial complex whose faces are the subsets $H \subseteq E(G)$ of the edge set of $G$ such that the degree of any vertex in the induced subgraph $G[H]$ is at most $r$. In this article, we give a closed form formula for the homotopy type of the $(n-2)$-matching complex of ...
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RNA‐centric world of retroviruses: unravelling the molecular strategies of genomic RNA packaging
Biological Reviews, EarlyView.ABSTRACT Retroviruses constitute a unique group of RNA viruses that have profoundly influenced both evolutionary trajectories and biomedical research. Their ability to reverse transcribe and integrate into host genomes has shaped genomic architecture across species and contributed to our understanding of oncogenes, gene regulation, and RNA biology ...
Mohammad Abdullah Jehad +5 more
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Locating-Chromatic Number of Bipartite Graphs
مجلة بغداد للعلومThe locating-chromatic number of a graph combines proper vertex coloring with vertex identification through distances to color classes. Although this parameter has been studied for many graph families, general results for bipartite graphs remain limited.
Dian Kastika Syofyan +5 more
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Bipartite Diametrical Graphs of Diameter 4 and Extreme Orders
International Journal of Mathematics and Mathematical Sciences, 2008 We provide a process to extend any bipartite diametrical graph of diameter 4 to an 𝑆-graph of the same diameter and partite sets. For a bipartite diametrical graph of diameter 4 and partite sets 𝑈 and 𝑊, where 2𝑚=|𝑈|≤|𝑊|, we prove that 2𝑚 is a sharp ...
Salah Al-Addasi, Hasan Al-Ezeh
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On Odd Covers of Cliques and Disjoint Unions
Journal of Graph Theory, EarlyView.ABSTRACT Babai and Frankl posed the “odd cover problem” of finding the minimum cardinality of a collection of complete bipartite graphs such that every edge of the complete graph of order n $n$ is covered an odd number of times. In a previous paper with O'Neill, some of the authors proved that this value is always ⌈ n / 2 ⌉ $\lceil n/2\rceil $ or ⌈ n /
Calum Buchanan +7 more
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Opuscula Mathematica, 2011 It has been shown in [S. Cichacz, A. Görlich, Decomposition of complete bipartite graphs into open trails, Preprint MD 022, (2006)] that any bipartite graph \(K_{a,b}\), is decomposable into open trails of prescribed even lengths.
Sylwia Cichacz, Agnieszka Görlich
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On the palette index of complete bipartite graphs
Discussiones Mathematicae Graph Theory, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mirko Hornák, Juraj Hudák
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Explicit 3‐colorings for Exponential Graphs
Journal of Graph Theory, EarlyView.ABSTRACT In 1985, El‐Zahar and Sauer showed that the chromatic number of the direct product of two 4‐chromatic graphs is 4, establishing a nontrivial case of Hedetniemi's conjecture, which has since been refuted in general. Their proof uses the concept of an exponential graph, showing that if a graph H $H$ has no proper 3‐coloring, then the exponential
Adrien Argento +2 more
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Random Generation and Enumeration of Bipartite Permutation Graphs [PDF]
, 2011 Connected bipartite permutation graphs without vertex labels are investigated. First, the number of connected bipartite permutation graphs of n vertices is given.
Yota Otachi +7 more
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