Hamiltonicity, independence number, and pancyclicity
نویسندگان
چکیده
منابع مشابه
Hamiltonicity, independence number, and pancyclicity
A graph on n vertices is called pancyclic if it contains a cycle of length ` for all 3 ≤ ` ≤ n. In 1972, Erdős proved that if G is a Hamiltonian graph on n > 4k vertices with independence number k, then G is pancyclic. He then suggested that n = Ω(k) should already be enough to guarantee pancyclicity. Improving on his and some other later results, we prove that there exists a constant c such th...
متن کاملA degree sum condition on the order, the connectivity and the independence number for Hamiltonicity
In [Graphs Combin. 24 (2008) 469–483.], the third author and the fifth author conjectured that if G is a k-connected graph such that σk+1(G) ≥ |V (G)|+κ(G)+(k−2)(α(G)−1), then G contains a Hamiltonian cycle, where σk+1(G), κ(G) and α(G) are the minimum degree sum of k + 1 independent ∗Supported by JSPS KAKENHI Grant Number 26800083. †Supported by JSPS KAKENHI Grant Number 26800086. ‡Supported b...
متن کاملOn the independence number and Hamiltonicity of uniform random intersection graphs
In the uniform random intersection graphs model, denoted by G n,m,λ , to each vertex v we assign exactly λ randomly chosen labels of some label set M of m labels and we connect every pair of vertices that has at least one label in common. In this model, we estimate the independence number α(G n,m,λ), for the wide, interesting range m = n α , α < 1 and λ = O(m 1/4). We also prove the hamiltonici...
متن کاملComplete Minors and Independence Number
Let G be a graph with n vertices and independence number α. Hadwiger’s conjecture implies that G contains a clique minor of order at least n/α. In 1982, Duchet and Meyniel proved that this bound holds within a factor 2. Our main result gives the first improvement on their bound by an absolute constant factor. We show that G contains a clique minor of order larger than .504n/α. We also prove rel...
متن کاملIndependence number and clique minors
Since χ(G) · α(G) ≥ |V (G)|, Hadwiger’s Conjecture implies that any graph G has the complete graph Kdn α e as a minor, where n is the number of vertices of G and α is the maximum number of independent vertices in G. Motivated by this fact, it is shown that any graph on n vertices with independence number α ≥ 3 has the complete graph Kd n 2α−2 e as a minor. This improves the well-known theorem o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2012
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2011.11.002