A graph is Hamiltonian if it contains a cycle that visits each vertex of the graph exactly once.A chord of a cycle C is an edge that joins two non-consecutive vertices of C.A graph of order n is chorded pancyclic if i...A graph is Hamiltonian if it contains a cycle that visits each vertex of the graph exactly once.A chord of a cycle C is an edge that joins two non-consecutive vertices of C.A graph of order n is chorded pancyclic if it contains a chorded cycle of length k for every integer k with 4≤k≤n.In 2018,Ferro and Lesniak gave an edge number conditon for the Hamiltonicity(and the chorded pancyclicity)of balanced and unbalanced k-partite graphs.In this paper,we extend the main results of Ferro and Lesniak,and provide an edge condition for the Hamiltonicity(and the chorded pancyclicity)of balanced and unbalanced k-partite graphs with given minimum degree,respectively.展开更多
Let k be an integer with k ≥ 2 and G a graph with order n 〉 4k. We prove that if the minimum degree sum of any two nonadjacent vertices is at least n ＋ k, then G contains a vertex cover with exactly k components su...Let k be an integer with k ≥ 2 and G a graph with order n 〉 4k. We prove that if the minimum degree sum of any two nonadjacent vertices is at least n ＋ k, then G contains a vertex cover with exactly k components such that k - 1 of them are chorded 4-cycles. The degree condition is sharp in general.展开更多
In this paper,the L_(p)chord Minkowski problem is concerned.Based on the results shown in[20],we obtain a new existence result of solutions to this problem in terms of smooth measures by using a nonlocal Gauss curvatu...In this paper,the L_(p)chord Minkowski problem is concerned.Based on the results shown in[20],we obtain a new existence result of solutions to this problem in terms of smooth measures by using a nonlocal Gauss curvature flow for p>−n with p≠0.展开更多
Chord measures are newly discovered translation-invariant geometric measures of convex bodies in Rn by Lutwak-Xi-Yang-Zhang(Communications on Pure and Applied Mathematics,2024),which is an extension of the surface are...Chord measures are newly discovered translation-invariant geometric measures of convex bodies in Rn by Lutwak-Xi-Yang-Zhang(Communications on Pure and Applied Mathematics,2024),which is an extension of the surface area measure.The Minkowski problems for chord measures was considered by Lutwak-Xi-Yang-Zhang.In this paper,we use variational method to solve the even Orlicz chord Minkowski problem.The obtained results are an extension of the even Orlicz Minkowski problem from Haberl-Lutwak-Yang-Zhang(Advances in Mathematics,2010).展开更多
Isoperimetric type inequalities for integral geometric invariants of random lines in the Euclidean space are shown.Entropy inequalities of probability densities on the affine Grassmann manifold of lines are given.
More than a simple concert pianist,Wilson Chu is an Indonesian musical diplomacy force.As a distinguished performer,composer,and educator,Wilson has left an indelible mark on the international stage by seamlessly blen...More than a simple concert pianist,Wilson Chu is an Indonesian musical diplomacy force.As a distinguished performer,composer,and educator,Wilson has left an indelible mark on the international stage by seamlessly blending Western classical music with Southeast Asian tradition.Since 2019,he has been the youngest Associate Professor of Piano at the College of Chinese and ASEAN Arts(CCAA)at Chengdu University,where he has dedicated himself to shaping the next generation of musicians.展开更多
文摘A graph is Hamiltonian if it contains a cycle that visits each vertex of the graph exactly once.A chord of a cycle C is an edge that joins two non-consecutive vertices of C.A graph of order n is chorded pancyclic if it contains a chorded cycle of length k for every integer k with 4≤k≤n.In 2018,Ferro and Lesniak gave an edge number conditon for the Hamiltonicity(and the chorded pancyclicity)of balanced and unbalanced k-partite graphs.In this paper,we extend the main results of Ferro and Lesniak,and provide an edge condition for the Hamiltonicity(and the chorded pancyclicity)of balanced and unbalanced k-partite graphs with given minimum degree,respectively.
基金Supported by Natural Science Foundation of China （Grant Nos. 11161035, 10801091）, Research Crants from Ningxia University （Grant No. （E）ndzr09-1） and Scientific Research Project in Xinjiang （Grant No. XJEDU2009S101）
文摘Let k be an integer with k ≥ 2 and G a graph with order n 〉 4k. We prove that if the minimum degree sum of any two nonadjacent vertices is at least n ＋ k, then G contains a vertex cover with exactly k components such that k - 1 of them are chorded 4-cycles. The degree condition is sharp in general.
基金supported by the National Natural Science Foundation of China(12171144,12231006,12122106).
文摘In this paper,the L_(p)chord Minkowski problem is concerned.Based on the results shown in[20],we obtain a new existence result of solutions to this problem in terms of smooth measures by using a nonlocal Gauss curvature flow for p>−n with p≠0.
基金Supported by the National Natural Science Foundation of China(12071277,12071334)。
文摘Chord measures are newly discovered translation-invariant geometric measures of convex bodies in Rn by Lutwak-Xi-Yang-Zhang(Communications on Pure and Applied Mathematics,2024),which is an extension of the surface area measure.The Minkowski problems for chord measures was considered by Lutwak-Xi-Yang-Zhang.In this paper,we use variational method to solve the even Orlicz chord Minkowski problem.The obtained results are an extension of the even Orlicz Minkowski problem from Haberl-Lutwak-Yang-Zhang(Advances in Mathematics,2010).
文摘Isoperimetric type inequalities for integral geometric invariants of random lines in the Euclidean space are shown.Entropy inequalities of probability densities on the affine Grassmann manifold of lines are given.
文摘More than a simple concert pianist,Wilson Chu is an Indonesian musical diplomacy force.As a distinguished performer,composer,and educator,Wilson has left an indelible mark on the international stage by seamlessly blending Western classical music with Southeast Asian tradition.Since 2019,he has been the youngest Associate Professor of Piano at the College of Chinese and ASEAN Arts(CCAA)at Chengdu University,where he has dedicated himself to shaping the next generation of musicians.
