Low independence number and Hamiltonicity implies 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 کاملSparse hypergraphs with low independence number
Let K (3) 4 denote the complete 3-uniform hypergraph on 4 vertices. Ajtai, Erdős, Komlós, and Szemerédi (1981) asked if there is a function ω(d) → ∞ such that every 3-uniform, K (3) 4 -free hypergraph H with N vertices and average degree d has independence number at least N d1/2 ω(d). We answer this question by constructing a 3-uniform, K (3) 4 -free hypergraph with independence number at most ...
متن کاملEdge number critical triangle free graphs with low independence numbers
The structure of all triangle free graphs G = (V,E) with |E|−6|V |+α(G) = 0 is determined, yielding an affirmative answer to a question of Stanis law Radziszowsky and Donald Kreher.
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: Journal of Graph Theory
سال: 2020
ISSN: 0364-9024,1097-0118
DOI: 10.1002/jgt.22553