منابع مشابه
Uniquely colorable mixed hypergraphs
A mixed hypergraph consists of two families of edges: the C-edges and D-edges. In a coloring every C-edge has at least two vertices of the same color, while every D-edge has at least two vertices colored differently. The largest and smallest possible numbers of colors in a coloring are termed the upper and lower chromatic number, χ̄ and χ, respectively. A mixed hypergraph is called uniquely colo...
متن کاملSaturated and weakly saturated hypergraphs
Lubell proved this by observing that the left-hand side is a probability: it is simply the probability that a maximal chain, chosen uniformly at random, intersects A. The LYM inequality implies that an antichain in P([n]) has size at most ( n bn/2c ) , the size of the ‘middle layer’ in P([n]). (This can also be proved by partitioning P([n]) into ( n bn/2c ) disjoint chains.) Bollobás’ Inequalit...
متن کاملUniquely Cycle-Saturated Graphs
Given a graph F , a graph G is uniquely F -saturated if F is not a subgraph of G and adding any edge of the complement to G completes exactly one copy of F . In this paper we study uniquely Ct-saturated graphs. We prove the following: (1) a graph is uniquely C5-saturated if and only if it is a friendship graph. (2) There are no uniquely C6-saturated graphs or uniquely C7-saturated graphs. (3) F...
متن کاملUniquely Kr-Saturated Graphs
A graph G is uniquely Kr-saturated if it contains no clique with r vertices and if for all edges e in the complement, G + e has a unique clique with r vertices. Previously, few examples of uniquely Kr-saturated graphs were known, and little was known about their properties. We search for these graphs by adapting orbital branching, a technique originally developed for symmetric integer linear pr...
متن کاملOrderings of uniquely colorable hypergraphs
For a mixed hypergraphH= (X,C,D), where C andD are set systems over the vertex set X, a coloring is a partition of X into ‘color classes’such that everyC ∈ Cmeets some class in more than one vertex, and everyD ∈ D has a nonempty intersection with at least two classes.A vertex-order x1, x2, . . . , xn onX (n=|X|) is uniquely colorable if the subhypergraph induced by {xj : 1 j i} has precisely on...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2018
ISSN: 1077-8926
DOI: 10.37236/7534