Extremed signed graphs for triangle

Wang, Dijian; Hou, Yaoping; Li, Deqiong

doi:10.48550/arxiv.2212.11460

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“…Let C − k be the set of all negative C k . For signed graphs, Wang, Hou and Li [29] determined the spectral Turán number of C − 3 . Denote by (G, +) (resp.…”

Section: Introductionmentioning

confidence: 99%

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School Mathematics Textbooks in China

Wang¹

2015

East China Normal University Scientific Reports

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Let µ and ν be two probability measures on R d , where µ(dx) = e −V (x) dx R d e −V (x) dx for some V ∈ C 1 (R d ). Explicit sufficient conditions on V and ν are presented such that µ * ν satisfies the log-Sobolev, Poincaré and super Poincaré inequalities. In particular, if V (x) = λ|x| 2 for some λ > 0 and ν(e λθ|•| 2 ) < ∞ for some θ > 1, then µ * ν satisfies the log-Sobolev inequality. This improves and extends the recent results on the log-Sobolev inequality derived in [20] for convolutions of the Gaussian measure and compactly supported probability measures. On the other hand, it is well known that the log-Sobolev inequality for µ * ν implies ν(e ε|•| 2 ) < ∞ for some ε > 0. RésuméDes conditions explicites suffisantes sur V et ν sont présentées telles que µ * ν satisfait des inégalités de Sobolev logarithmique, de Poincaré et de super-Poincaré. En particulier, si V (x) = λ|x| 2 pour quelque λ > 0 et ν(e λθ|•| 2 ) < ∞ avec θ > 1, alors µ * ν satisfait l'inégalité de Sobolev logarithmique. Cela améliore et étend des résultats récents sur l'inégalité de Sobolev logarithmique obtenus dans [20] pour des convolutions de la mesure de Gauss et des mesures de probabilité à support compact. D'autre part, il est bien connu que l'inégalité de Sobolev logarithmique pour µ * ν implique ν(e ε|•| 2 ) < ∞ pour quelque ε > 0.

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“…Let C − k be the set of all negative C k . For signed graphs, Wang, Hou and Li [29] determined the spectral Turán number of C − 3 . Denote by (G, +) (resp.…”

Section: Introductionmentioning

confidence: 99%

“…

Let C − k be the set of all negative C k . For odd cycle, Wang, Hou and Li [29] gave a spectral condition for the existence of negative C 3 in unbalanced signed graphs. For even cycle, we determine the maximum index among all C − 4 -free unbalanced signed graphs and completely characterize the extremal signed graph in this paper.

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confidence: 99%

School Mathematics Textbooks in China

Wang¹

2015

East China Normal University Scientific Reports

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Extremed signed graphs for triangle

Cited by 1 publication

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School Mathematics Textbooks in China

School Mathematics Textbooks in China

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