Let r > 1 be an integer. An h-hypergraph H is said to be r-quasi-linear (linear for r = 1) if any two edges of H intersect in 0 or r vertices. In this paper it is shown that r-quasi-linear paths P h,r m of length m > 1 and cycles C h,r m of length m > 3 are chromatically unique in the set of h-uniform r-quasi-linear hypergraphs provided r > 2 and h > 3r − 1.

The zero-divisor graph Π(R) of a commutative ring R is the whose vertices are elements such that u and v adjacent if only uv = 0. If graphs G H have same chromatic polynomial, then we say they chromatically equivalent (or χ−equivalent), written as ∼ H. Suppose uniquely determined by its polynomial. Then it said to be unique χ-unique). In this paper, discuss question: For which numbers n Π(Zn) χ...

In order to assess the relative contributions of chromatic vs luminance information to motion processing in infants, we employed a motion:detection (M:D) paradigm. Stimuli consisted of 27 deg by 40 deg, 0.25 c/deg sinusoidal gratings moving at 22 deg/sec (5.6 Hz), and were either chromatically defined or luminance-defined. Contrast thresholds for direction-of-motion (M) were obtained using a di...

In this paper, we discuss a pair of chromatically equivalent of K4-homeomorphs of girth 11, that is, K4(1, 3, 7, d, e, f) and K4(1, 3, 7, d′, e′, f ′). As a result, we obtain two infinite chromatically equivalent non-isomorphic K4-homeomorphs. Mathematical Subject Classification: 05C15

A graph G is chromatically k–connected if every vertex cutset induces a subgraph with chromatic number at least k. Thus, in particular each neighborhood has to induce a k–chromatic subgraph. In [3], Godsil, Nowakowski and Nešetřil asked whether there exists a k–chromatically connected graph such that every minimal cutset induces a subgraph with no triangles. We show that the answer is positive ...

If G is a graph, a G-decomposition of a host graph H is a partition of the edges of H into subgraphs of H which are isomorphic to G. The chromatic index of a Gdecomposition of H is the minimum number of colors required to color the parts of the decomposition so that parts which share a common node get different colors. We establish an upper bound on the chromatic index and characterize those de...

Let (G) denote the minimum real root of the -polynomial of the complement of a graph G and (G) the minimum degree of G. In this paper, we give a characterization of all connected graphs G with (G)¿−4. Using these results, we establish a su5cient and necessary condition for a graph G with p vertices and (G)¿p− 3, to be chromatically unique. Many previously known results are generalized. As a byp...

Abstract. For integers p, q, s with p ≥ q ≥ 2 and s ≥ 0, let K−s 2 (p, q) denote the set of 2−connected bipartite graphs which can be obtained from Kp,q by deleting a set of s edges. In this paper, we prove that for any graph G ∈ K−s 2 (p, q) with p ≥ q ≥ 3 and 1 ≤ s ≤ q−1, if the number of 3-independent partitions of G is 2p−1 + 2q−1 + s + 4, then G is chromatically unique. This result extends...

For integers p, q, s with p ≥ q ≥ 2 and s ≥ 0, let K−s 2 (p, q) denote the set of 2−connected bipartite graphs which can be obtained from Kp,q by deleting a set of s edges. F.M.Dong et al. (Discrete Math. vol.224 (2000) 107–124) proved that for any graph G ∈ K−s 2 (p, q) with p ≥ q ≥ 3 and 0 ≤ s ≤ min{4, q−1}, then G is chromatically unique. In this paper, we shall extend this result to p ≥ q ≥...