设P(G,λ)是图G的色多项式.如果对任意使P(G,λ)=P(H,λ)的图H都与G同构,则称图G是色唯一图.通过比较图的特征子图的个数,讨论了由文献[Koh K M,Teo K L.The search for chromatically unique graphs.Graphs and Combinatorics,1999,6:2...设P(G,λ)是图G的色多项式.如果对任意使P(G,λ)=P(H,λ)的图H都与G同构,则称图G是色唯一图.通过比较图的特征子图的个数,讨论了由文献[Koh K M,Teo K L.The search for chromatically unique graphs.Graphs and Combinatorics,1999,6:259-285]中提出的猜想(若n≥k+2,则完全三部图K(n-k,n,n)是色唯一图);推广了文献[Liu Ru-yin,Zhao Hai-xing,Ye Cheng-fu.A complete solution to a conjecture on chromatic unique of complete tripartite graphs.Discrete Mathematics,2004,289:175-179]中的结果(若n≥k+2≥4,则K(n-k,n,n)是色唯一图;若n≥2k≥4,则K(n-k,n-1,n)是色唯一图);证明了若n≥k+2≥4,则K(n-k,n,…,n)是色唯一图,若n≥k+2≥4,则K(n-k,n-1,n,…,n)是色唯一图.展开更多
For every integer 4≤d≤11,an explicit construction of infinite families of 2d-regular unique-neighbor expanders is presented,which is a generalization of the 6-regular unique-neighbors initially developed by Alon and...For every integer 4≤d≤11,an explicit construction of infinite families of 2d-regular unique-neighbor expanders is presented,which is a generalization of the 6-regular unique-neighbors initially developed by Alon and Capalbo.Additionally,for values of d greater than 11,a sufficient condition is established for employing the same construction method.Our construction method involves the“line product”of large bipartite Ramanujan graphs and a sufficiently good unique-neighbor expander(a small gadget).展开更多
文摘设P(G,λ)是图G的色多项式.如果对任意使P(G,λ)=P(H,λ)的图H都与G同构,则称图G是色唯一图.通过比较图的特征子图的个数,讨论了由文献[Koh K M,Teo K L.The search for chromatically unique graphs.Graphs and Combinatorics,1999,6:259-285]中提出的猜想(若n≥k+2,则完全三部图K(n-k,n,n)是色唯一图);推广了文献[Liu Ru-yin,Zhao Hai-xing,Ye Cheng-fu.A complete solution to a conjecture on chromatic unique of complete tripartite graphs.Discrete Mathematics,2004,289:175-179]中的结果(若n≥k+2≥4,则K(n-k,n,n)是色唯一图;若n≥2k≥4,则K(n-k,n-1,n)是色唯一图);证明了若n≥k+2≥4,则K(n-k,n,…,n)是色唯一图,若n≥k+2≥4,则K(n-k,n-1,n,…,n)是色唯一图.
文摘For every integer 4≤d≤11,an explicit construction of infinite families of 2d-regular unique-neighbor expanders is presented,which is a generalization of the 6-regular unique-neighbors initially developed by Alon and Capalbo.Additionally,for values of d greater than 11,a sufficient condition is established for employing the same construction method.Our construction method involves the“line product”of large bipartite Ramanujan graphs and a sufficiently good unique-neighbor expander(a small gadget).
