Chromatic bounds for some classes of 2K2-free graphs

Chromatic bounds for some classes of 2K2-free graphs

A hereditary class G of graphs is χ-bounded if there is a χ-binding function, say f such that χ(G) ≤ f(ω(G)), for every G ∈ G, where χ(G) (ω(G)) denote the chromatic (clique) number of G. It is known that for every 2K2-free graph G, χ(G) ≤ ( ω(G)+1 2 ) , and the class of (2K2, 3K1)-free graphs does not admit a linear χ-binding function. In this paper, we are interested in classes of 2K2-free gr...

Some lower bounds for the $L$-intersection number of graphs

‎For a set of non-negative integers~$L$‎, ‎the $L$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $A_v subseteq {1,dots‎, ‎l}$ to vertices $v$‎, ‎such that every two vertices $u,v$ are adjacent if and only if $|A_u cap A_v|in L$‎. ‎The bipartite $L$-intersection number is defined similarly when the conditions are considered only for the ver...

Closure of K1 + 2K2-free graphs

Chromatic Equivalence Classes of Some Families of Complete Tripartite Graphs

We obtain new necessary conditions on a graph which shares the same chromatic polynomial as that of the complete tripartite graph Km,n,r. Using these, we establish the chromatic equivalence classes for K1,n,n+1 (where n ≥ 2). This gives a partial solution to a question raised earlier by the authors. With the same technique, we further show that Kn−3,n,n+1 is chromatically unique if n ≥ 5. In th...

Some bounds on chromatic number of NI graphs

A connected graph is called neighbourly irregular (NI) if it contains no edge between the vertices of the same degree. In this paper we determine the upper bound for chromatic number of a neighbourly irregular graph. We also prove some results on neighbourly irregular graphs and its chromatic number.