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8 votes
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What is the best lower bound for the domination number in regular graphs of girth 5?

The following theorem is a classical result (see [Alon and Spencer, The probabilistic method, 2nd ed., Theorem 1.2.2]): Theorem: Let $G$ be a graph on $n$ vertices with minimum degree $d$. Then $G$ ...
Florent Foucaud's user avatar
7 votes
0 answers
97 views

What is known about chromatic polynomial of hypergraph at $-1$

Let $H$ be a hypergraph and let $P_H$ denote its chromatic polynomial. I am interested in the best results interpreting $P_H(-1)$. I am interested both in the general case (which I think is hard) as ...
John Machacek's user avatar
2 votes
0 answers
50 views

An equation involving fractional covering number of hypergraphs

Let $\mathcal{H}=(S,\mathcal{X})$ be a hypergraph, where $S = \{ s_1, \ldots, s_n \}$, and $\mathcal{X} = \{ X_1, \ldots, X_m \}$. The dual hypergraph $\mathcal{H}^*$ of $\mathcal{H}$ is the ...
Victor's user avatar
  • 655
1 vote
0 answers
315 views

Definition of k-partite hypergraph

I would like to know the standard definition of k-partite hypergraph. There are two natural generalizations of k-partite graph to k-partite hypergraph: 1. For all edges e, any two vertices in e are ...
Boonpipop Sirirojrattana's user avatar
0 votes
0 answers
97 views

Shortest hyperpath algorithm in intuitionistic fuzzy hypergraphs

I was looking for an algorithm to calculate the shortest hyperpath in intuitionistic fuzzy hypergraphs and I found only this article (which propose two algorithms). Are there any others algorithms ...
Bilal's user avatar
  • 101
0 votes
0 answers
71 views

products/factoring of two hypergraphs with same vertex set?

all the basic products for graphs have been extended to hypergraphs[1]. is there a concept of a product of hypergraphs with the same vertex set? has this been studied? normally the hypergraph ...
vzn's user avatar
  • 529