WebJul 1, 2011 · The Gallai–Edmonds Decomposition of G is the partition of V (G) into the three sets A, C, D. A graph G is factor-critical if every subgraph obtained by deleting one vertex has a 1-factor. A matching in G is near-perfect if it covers all but one vertex of G. For S ⊆ V (G), let G [S] denote the subgraph of G induced by S. Theorem 5 Gallai ... WebJan 1, 2024 · In this paper, some new results on the matching number are obtained: (i) For k-uniform hypergraphs, some inequalities involving the matching number and the edge covering number are proved, which is a generalization of Gallai Theorem from graphs to k-uniform hypergraphs.(ii) For k-uniform hypertrees, a sufficient and necessary condition …
Title: Extensions of Erdős-Gallai Theorem and Luo
WebApr 17, 2009 · A central theorem in the theory of graphic sequences is due to P. Erdos and T. Gallai. Here, we give a simple proof of this theorem by induction on the sum of the sequence. Type WebThis theorem, implicit in [4] and [6], is quoted explicitly in [8]. Our purpose in the present paper is to show that the Edmonds--Gallai decom- position generalizes to locally finite graphs. Our proof yields a short derivation of the Edmonds--Gallai theorem from Tutte's 1-Factor Theorem [13] in the finite case. hot 2020 christmas toys
What are Sylvester-Gallai configurations in the complex projective …
WebApr 12, 2024 · This answers affirmatively two conjectures of Gupta [ECCC 2014] that were raised in the context of solving certain depth- polynomial identities. To obtain our main theorems we prove a new result classifying the possible ways that a quadratic polynomial can vanish when two other quadratic polynomials vanish. WebThe original Erd}os-Gallai Theorem The Erd}os-Gallai Theorem is a fundamental, classic result that tells you when a sequence of integers occurs as the sequence of degrees of a … WebFeb 20, 2024 · Remark: In higher dimension, it is known that the configuration of points has to be coplanar. If the points have coordinates defined over $\mathbb{R}$, the Sylvester-Gallai theorem shows that any configuration as above is in fact collinear. Over finite fields one can of course find plenty of configurations by taking all points. hot 20s caracteristicas