منابع مشابه
Chromatically Unique Multibridge Graphs
Let θ(a1, a2, · · · , ak) denote the graph obtained by connecting two distinct vertices with k independent paths of lengths a1, a2, · · · , ak respectively. Assume that 2 ≤ a1 ≤ a2 ≤ · · · ≤ ak. We prove that the graph θ(a1, a2, · · · , ak) is chromatically unique if ak < a1 + a2, and find examples showing that θ(a1, a2, · · · , ak) may not be chromatically unique if ak = a1 + a2.
متن کاملClasses of chromatically unique graphs
Borowiecki, M. and E. Drgas-Burchardt, Classes of chromatically unique graphs, Discrete Mathematics Ill (1993) 71-75. We prove that graphs obtained from complete equibipartite graphs by deleting some independent sets of edges are chromatically unique. 1. Preliminary definitions and results In this paper we consider finite, undirected, simple and loopless graphs. Two graphs G and H are said to b...
متن کاملChromatically Supremal Decompositions of Graphs
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...
متن کاملOn k-chromatically connected graphs
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 ...
متن کاملChromatically Unique Bipartite Graphs with Certain 3-independent Partition Numbers II
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1979
ISSN: 0012-365X
DOI: 10.1016/0012-365x(79)90107-9