Ramsey oscillations typically exhibit an exponential decay envelope due to environmental noise. However,recent experiments have observed nonmonotonic Ramsey fringes characterized by beating patterns, which deviate fro...Ramsey oscillations typically exhibit an exponential decay envelope due to environmental noise. However,recent experiments have observed nonmonotonic Ramsey fringes characterized by beating patterns, which deviate from the standard behavior. These beating patterns have primarily been attributed to charge-noise fluctuations.In this paper, we have experimentally observed Ramsey fringe with beating pattern for transmon qubits, and traced the origin to electric instruments induced flux noise.展开更多
For k given graphs H_(1),...,H_(k) with k≥2,the k-color Ramsey number R(H_(1),...,H_(k)) represents the minimum integer N with the following property:if the edges of the complete graph K_(N) are colored with k colors...For k given graphs H_(1),...,H_(k) with k≥2,the k-color Ramsey number R(H_(1),...,H_(k)) represents the minimum integer N with the following property:if the edges of the complete graph K_(N) are colored with k colors,then there exists some i with 1≤i≤k such that K_(N) has a subgraph in color i isomorphic to H_(i).Let C_(m) be a cycle of length m and K_(1,n) a star of order n+1.In this paper,we systematically introduce the latest research progress on star-quadrilateral Ramsey numbers and provide an overview of Ramsey numbers concerning quadrilaterals,including multicolor cases.展开更多
Given two graphs G and H,the Ramsey number R(G,H)is the smallest positive integer N such that every 2-coloring of the edges of K_(N)contains either a red G or a blue H.Let K_(N-1)■K_(1,k)be the graph obtained from K_...Given two graphs G and H,the Ramsey number R(G,H)is the smallest positive integer N such that every 2-coloring of the edges of K_(N)contains either a red G or a blue H.Let K_(N-1)■K_(1,k)be the graph obtained from K_(N-1)by adding anew vertexνconnecting k vertices of K_(N-1).A graph G withχ(G)=k+1 is called edge-critical if G contains an edge e such thatχ(G-e)=k.A considerable amount of research has been conducted by previous scholars on Ramsey numbers ofgraphs.In this study,we show that for an edge-critical graph G with x(G)=k+1,when k≥2,1≥2,and n is sufficiently large,R(G,K_(1)+nK_(t))=knt+1 and r,(G,K_(1)+nK_(t))=(k-1)nt+1.展开更多
Given a graph F and a positive integer r,the size Ramsey number R(F,r)is defined as the smallest integer m such that there exists a graph G with m edges where every r-color edge coloring of G results in a monochromati...Given a graph F and a positive integer r,the size Ramsey number R(F,r)is defined as the smallest integer m such that there exists a graph G with m edges where every r-color edge coloring of G results in a monochromatic copy of F.Let P_(n)and C_(n)represent a path and a cycle on n vertices,respectively.In this paper,we establish that for sufficiently large n,R(P_(n),P_(n),P_(n))<772n.Furthermore,we demonstrate that for sufficiently large even integers n,R(P_(n),P_(n),C_(n))≤17093n.For sufficiently large odd integer n,we show that R(P_(n),P_(n),C_(n))≥(7.5-o(1))n.展开更多
For given simple graphs H1,H2,...,Hc,the multicolor Ramsey number R(H1,H2,...,Hc) is defined as the smallest positive integer n such that for an arbitrary edge-decomposition{Gi}ci=1of the complete graph K_n,at least o...For given simple graphs H1,H2,...,Hc,the multicolor Ramsey number R(H1,H2,...,Hc) is defined as the smallest positive integer n such that for an arbitrary edge-decomposition{Gi}ci=1of the complete graph K_n,at least one Gihas a subgraph isomorphic to Hi.Let m,n1,n2,...,nc be positive integers andΣ=Σci=1(ni-1).Some bounds and exact values of R(K1,n1,...,K1,nc,Pm) have been obtained in literature.Wang (Graphs Combin.,2020) conjectured that ifΣ?≡0 (mod m-1) andΣ+1≥(m-3)2,then R(K1,n1,...,K1,nc,Pm)=Σ+m-1.In this note,we give a new lower bound and some exact values of R(K1,n1,...,K1,nc,Pm) provided m≤Σ,Σ≡k (mod m-1),and 2≤k≤m-2.These results partially confirm Wang’s conjecture.展开更多
文摘Ramsey oscillations typically exhibit an exponential decay envelope due to environmental noise. However,recent experiments have observed nonmonotonic Ramsey fringes characterized by beating patterns, which deviate from the standard behavior. These beating patterns have primarily been attributed to charge-noise fluctuations.In this paper, we have experimentally observed Ramsey fringe with beating pattern for transmon qubits, and traced the origin to electric instruments induced flux noise.
基金supported by NSFC(Nos.12161141003,11931006)supported by NSFC(Nos.11801520,12171436,12271489)supported by NSFC(No.11601527)。
文摘For k given graphs H_(1),...,H_(k) with k≥2,the k-color Ramsey number R(H_(1),...,H_(k)) represents the minimum integer N with the following property:if the edges of the complete graph K_(N) are colored with k colors,then there exists some i with 1≤i≤k such that K_(N) has a subgraph in color i isomorphic to H_(i).Let C_(m) be a cycle of length m and K_(1,n) a star of order n+1.In this paper,we systematically introduce the latest research progress on star-quadrilateral Ramsey numbers and provide an overview of Ramsey numbers concerning quadrilaterals,including multicolor cases.
基金supported by the National Key Research and Development Program of China(2023YFA1010200,2020YFA0713100)the National Natural Science Foundation of China(12071453)the Innovation Program for Quantum Science and Technology(2021ZD0302902).
文摘Given two graphs G and H,the Ramsey number R(G,H)is the smallest positive integer N such that every 2-coloring of the edges of K_(N)contains either a red G or a blue H.Let K_(N-1)■K_(1,k)be the graph obtained from K_(N-1)by adding anew vertexνconnecting k vertices of K_(N-1).A graph G withχ(G)=k+1 is called edge-critical if G contains an edge e such thatχ(G-e)=k.A considerable amount of research has been conducted by previous scholars on Ramsey numbers ofgraphs.In this study,we show that for an edge-critical graph G with x(G)=k+1,when k≥2,1≥2,and n is sufficiently large,R(G,K_(1)+nK_(t))=knt+1 and r,(G,K_(1)+nK_(t))=(k-1)nt+1.
基金Supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(Grant No.24KJD110008)the National Natural Science Foundation of China(Grant No.12401469)。
文摘Given a graph F and a positive integer r,the size Ramsey number R(F,r)is defined as the smallest integer m such that there exists a graph G with m edges where every r-color edge coloring of G results in a monochromatic copy of F.Let P_(n)and C_(n)represent a path and a cycle on n vertices,respectively.In this paper,we establish that for sufficiently large n,R(P_(n),P_(n),P_(n))<772n.Furthermore,we demonstrate that for sufficiently large even integers n,R(P_(n),P_(n),C_(n))≤17093n.For sufficiently large odd integer n,we show that R(P_(n),P_(n),C_(n))≥(7.5-o(1))n.
基金National Natural Science Foundation of China (Grant No. 12071453)the National Key R and D Program of China (Grant No. 2020YFA0713100)the Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0302902)。
文摘For given simple graphs H1,H2,...,Hc,the multicolor Ramsey number R(H1,H2,...,Hc) is defined as the smallest positive integer n such that for an arbitrary edge-decomposition{Gi}ci=1of the complete graph K_n,at least one Gihas a subgraph isomorphic to Hi.Let m,n1,n2,...,nc be positive integers andΣ=Σci=1(ni-1).Some bounds and exact values of R(K1,n1,...,K1,nc,Pm) have been obtained in literature.Wang (Graphs Combin.,2020) conjectured that ifΣ?≡0 (mod m-1) andΣ+1≥(m-3)2,then R(K1,n1,...,K1,nc,Pm)=Σ+m-1.In this note,we give a new lower bound and some exact values of R(K1,n1,...,K1,nc,Pm) provided m≤Σ,Σ≡k (mod m-1),and 2≤k≤m-2.These results partially confirm Wang’s conjecture.
