Chvátal's Condition cannot hold for both a graph and its complement

Chvátal's Condition cannot hold for both a graph and its complement

Chvátal’s Condition is a sufficient condition for a spanning cycle in an n-vertex graph. The condition is that when the vertex degrees are d1, . . . , dn in nondecreasing order, i < n/2 implies that di > i or dn−i ≥ n − i. We prove that this condition cannot hold in both a graph and its complement, and we raise the problem of finding its asymptotic probability in the random graph with edge prob...

On the Connectivity of a Graph and its Complement Graph

In this paper, we study the connectivity of the complement of a graph. We first establish a simple formula to compute the connectivity of a graph that comes from the join of graphs. Base on this formula, we give an upper and a lower bound to the connectivity of the complement of a graph. Keyword: connectivity, complement, join, vertex of attachment.

graphs cospectral with a friendship graph or its complement

let $n$ be any positive integer and let $f_n$ be the friendship (or dutch windmill) graph with $2n+1$ vertices and $3n$ edges. here we study graphs with the same adjacency spectrum as the $f_n$. two graphs are called cospectral if the eigenvalues multiset of their adjacency matrices are the same. let $g$ be a graph cospectral with $f_n$. here we prove that if $g$ has no cycle of length $4$ or $...

A bound on the order of a graph when both the graph and its complement are contraction-critically k-connected

designing and validating a textbook evaluation questionnaire for reading comprehension ii and exploring its relationship with achievement

در هر برنامه آموزشی، مهم ترین فاکتور موثر بر موفقیت دانش آموزان کتاب درسی است (مک دونو و شاو 2003). در حقیقت ، کتاب قلب آموزش زبان انگلیسی است( شلدن 1988). به دلیل اهمیت والای کتاب به عنوان عنصر ضروری کلاس های آموزش زبان ، کتب باید به دقت ارزیابی و انتخاب شده تا از هرگونه تاثیر منفی بر دانش آموزان جلوگیری شود( لیتز). این تحقیق با طراحی پرسش نامه ارزیابی کتاب که فرصت ارزیابی معتبر را به اساتید د...