Apr 22, 2014 · A partial order relation in the set G ( n , k ) of graphs of order n and chromatic number k can be defined as follows: Let G and H be two ...

Oct 22, 2024 · In this paper the greatest [n/2] values of P(G; 3) in the class of connected 3-chromatic graphs G of order n are found, where P(G; ...

This paper is focused on the (⌈n/2⌉ + 2)-nd level and it is shown that this level contains (n2 −2n+4)/4 bicyclic graphs for even n and (n+1)2/4 bicyclic graphs.

Jul 1, 2003 · In this paper the first ⌈ n-2 ⌉ levels of the diagram of the partially ordered set of connected 3-chromatic graphs of order n are described.

Dec 25, 2023 · Abstract: We define an extremal (r|χ)-graph as an r-regular graph with chromatic number χ of minimum order. We show that the Turán graphs Tak,k, ...

Extremal Bicyclic 3-Chromatic Graphs. Ioan Tomescu; Sana Javed. Original Paper 22 April 2014 Pages: 1043 - 1052. Uniquely Derived Generalized Line Graphs and ...

The basic statement of extremal graph theory is Mantel's theorem, proved in 1907, which states that any graph on n vertices with no triangle contains at ...

In the set of graphs of order n and chromatic number k the following partial order relation is defined. One says that a graph G is less than a graph H if ...

The chromatic number χ(G) of a graph. G is the minimum number of colors such that G can be colored with these colors in such a way that no two adjacent vertices ...