A sharp refinement of a result of Alon, Ben-Shimon and Krivelevich on bipartite graph vertex sequences
نویسندگان
چکیده
We give a sharp refinement of a result of Alon, Ben-Shimon and Krivelevich. This gives a sufficient condition for a finite sequence of positive integers to be the vertex degree list of both parts of a bipartite graph. The condition depends only on the length of the sequence and its largest and smallest elements.
منابع مشابه
A note on regular Ramsey graphs
We prove that there is an absolute constant C > 0 so that for every natural n there exists a trianglefree regular graph with no independent set of size at least C √ n log n.
متن کاملA better tester for bipartiteness?
Alon and Krivelevich (SIAM J. Discrete Math. 15(2): 211-227 (2002)) show that if a graph is ε-far from bipartite, then the subgraph induced by a random subset of Õ(1/ε) vertices is bipartite with high probability. We conjecture that the induced subgraph is Ω̃(ε)-far from bipartite with high probability. Gonen and Ron (RANDOM 2007) proved this conjecture in the case when the degrees of all vertic...
متن کاملRandom regular graphs of non-constant degree: Concentration of the chromatic number
In this work we show that with high probability the chromatic number of a graph sampled from the random regular graph model Gn,d for d = o(n ) is concentrated in two consecutive values, thus extending a previous result of Achlioptas and Moore. This concentration phenomena is very similar to that of the binomial random graph model G(n, p) with p = d n . Our proof is largely based on ideas of Alo...
متن کاملThe Choice Number of Random Bipartite Graphs
A random bipartite graph G n n p is obtained by taking two disjoint subsets of vertices A and B of cardinality n each, and by connecting each pair of vertices a ! A and b ! B by an edge randomly and independently with probability p " p n . We show that the choice number of G n n p is, almost surely, 1 # o 1 log2 np for all values of the edge probability p " p n , where the o 1 term tends to 0 a...
متن کاملGroups whose Bipartite Divisor Graph for Character Degrees Has Five Vertices
Let $G$ be a finite group and $cd^*(G)$ be the set of nonlinear irreducible character degrees of $G$. Suppose that $rho(G)$ denotes the set of primes dividing some element of $cd^*(G)$. The bipartite divisor graph for the set of character degrees which is denoted by $B(G)$, is a bipartite graph whose vertices are the disjoint union of $rho(G)$ and $cd^*(G)$, and a vertex $p in rho(G)$ is conne...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 60 شماره
صفحات -
تاریخ انتشار 2014