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An often-ignored Humean contribution to Scottish Enlightenment is ‘conjectural history’, an eighteenth-century historical genre that attempted to trace the origins and development of particular institutions from prehistory to modernity.
Juan Samuel Santos Castro
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On the double-critical graph conjecture
Discrete Mathematics, Algorithms and Applications, 2022A connected graph [Formula: see text] is double-critical if the chromatic number of [Formula: see text] is two less than that of [Formula: see text] whenever [Formula: see text] and [Formula: see text] are two adjacent vertices of [Formula: see text].
R. Dharmarajan, D. Ramachandran
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Minkowsky's conjecture on the critical determinant
Cybernetics, 1986The authors investigate Minkowski's famous conjecture on the critical determinant of the domain \(| x|^ p+| y|^ p1\) with the help of a computer. They show that their computer-results support Minkowski's conjecture in particular at the critical regions \(p=1+\epsilon_ 1\) and \(p=2\pm \epsilon_ 2\) for small \(\epsilon_ 1,\epsilon_ 2>0\).
Glazunov, N. M., Malyshev, A. V.
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The rise and fall of the critical graph conjecture
Journal of Graph Theory, 1983AbstractIn this expository paper we discuss the critical graph conjecture and its eventual disproof by M.K. Goldberg and others.
Amanda G. Chetwynd, Robin J. Wilson
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On the critical graph conjecture
Journal of Graph Theory, 1980AbstractGol'dberg has recently constructed an infinite family of 3‐critical graphs of even order. We now prove that if there exists a p(≥4)‐critical graph K of odd order such that K has a vertex u of valency 2 and another vertex v ≠ u of valency ≤(p + 2)/2, then there exists a p‐critical graph of even order.
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Three Conjectures on Critical Graphs
The American Mathematical Monthly, 1976(1976). Three Conjectures on Critical Graphs. The American Mathematical Monthly: Vol. 83, No. 2, pp. 128-129.
Robin J. Wilson, Lowell W. Beineke
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A conjecture on k-factor-critical and 3-γ-critical graphs
Science China Mathematics, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Tao, Yu, Qinglin
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Mader’s Conjecture On Extremely Critical Graphs
Combinatorica, 2006A non-complete graph G is called an (n,k)-graph if it is n-connected but G—X is not (n−|X|+1)-connected for any X ⊂ V (G) with |X|≤k. Mader conjectured that for k≥3 the graph K2k+2−(1−factor) is the unique (2k,k)-graph(up to isomorphism).Here we prove this conjecture.
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