Siemion Fajtlowicz

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Let G=G(n) be a graph of n vertices. Let X=X(G) denote its chromatic number and a=o(G) the largest integer I so that G contains a subdivision of K, i.e . a(G)=1 is the largest integer such that G contains a subgraph homeomorphic with complete graph of l vertices . Let us put H(G)= X(G) and H(n)=max H(G(n)) o (G) G(n) Hajós [10] conjectured that H(n)=1 and(More)
The independence number of the graph of a fullerene, the size of the largest set of vertices such that no two are adjacent (corresponding to the largest set of atoms of the molecule, no pair of which are bonded), appears to be a useful selector in identifying stable fullerene isomers. The experimentally characterized isomers with 60, 70 and 76 atoms(More)
We shall discuss here some cases in which (1) becomes an equality. 2 Theorem. I f q ~ p then = implies that 3 q 2 p . ~ 5 . For all natural numbers n p + q Pl and ql such that 3 q l 2 p l = 5 there is a unique connected graph G with P = P l , ~t 2 q=q~ a n d = ~ . n p + q 2 1. Since graphs satisfying = must have a large chromatic number n p + q and a high(More)
We discuss a conjecture of J. R. Griggs relating the maximum number of leaves in a spanning tree of a simple, connected graph to the order and independence number of the graph. We prove a generalization of this conjecture made by the computer program Graffiti, and discuss other similar conjectures, including several generalizations of the theorem that the(More)
In August 2003 the computer program GRAFFITI made conjecture 1001 stating that for any benzenoid graph, the size of a maximum matching equals the number of positive eigenvalues. Later, the authors learned that this conjecture was already known in 1982 to I. Gutman (Kragujevac). Here we present a proof of this conjecture and of a related theorem. The results(More)