The problem of finding a formula for the clique number of the Paley graph G*(p) where p is a prime number such that p 1(mod 4) seems to be a hard one. These clique numbers are known for the caws 5 p 1601. In this paper we show that the clique number and chromatic number of ...
Kotlov, Rank, term rank, and chromatic number, Discrete Math. 250 (2002) 253–257. [4] D.G. Hoffman, P.D. Johnson, On the choice number of Km,n, Congr. Numer. 98 (1993) 105–111. [5] A. Kotlov, Rank and chromatic number of a graph, J. Graph Theory 26 (1997) 1–8. [...
The lower clique number may be similarly defined as the size of a graph's smallest maximal clique. For an arbitrary graph, (1) where is the vertex degree of . The clique number of a graph is equal to the independence number of the complement graph, (2) The chromatic number of...
The vertex colouring problem (VCP) calls for determining the minimum number of colour-classes in any feasible vertex colouring, i.e., to determine the chromatic number χ(G) of the graph. We refer the interested reader to Malaguti & Toth (2010) for further details on the VCP. A (vertex...
Summary: The clique-chromatic number of a graph $G = (V,E)$ denoted by $χ_{c }(G)$ is the smallest integer $k$ such that there exists a partition of the vertex set of $G$ into $k$ subsets with the property that no maximal clique of $G$ is contained in any of the subsets...
ω, ∆ and χ. J. Graph Theory 27 (1998) 177–212. 14]]>Claw-free graphsChromatic numberList coloringChudnovsky and Seymour proved that every connected claw-free graph that contains a stable set of size 3 has chromatic number at most twice its clique number. We improve this for small ...
We give a linear time algorithm to find a maximum clique of a chordal graph and also will show that the size of a maximum clique of a chordal graph equals the chromatic number of the graph, i.e., we can color the whole graph with the number of colors equal to the size of a ...
(Summary).JO - Aequationes mathematicaePY - 1993VL - 45IS - 2-3SP - 122EP - 122LA - engKW - critical graphs; independence number; clique number... S Klavzar 被引量: 11发表: 1993年 Clique minors in double-critical graphs A connected t-chromatic graph G is double-critical Rolek,Mart...
G - graph size - (optional) integer or range; size of clique to find Description • FindCliquereturns a list of vertices which comprise acliquein the graphG. The optional parametersizespecifies a size for the clique. Ifsizeis omitted,FindCliquebehaves identically toMaximumCliqueand returns a...
Then the fractional strong chromatic index of G is at most 1.75ΔG2. 2. Upper bound on the clique number of the square of the line graph of G For any two different edges from a graph G we define distG(e,f) as the number of edges in the shortest path between e and f plus 1,...