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# why what type is the graph reduced from k-regular hypergraph?

5 added 46 characters in body  A hypergraph $$H = (V,E)$$ consists of a set $$V = \{v_1, v_2, \cdots, v_n\}$$ of vertices and a set $$E = \{e_1, e_2, \cdots , e_m\}$$ of edges, each being a subset of $$V$$. If each $$|V| = 2$$, H is a general graph.

The degree $$d(v)$$ of a vertex v is the number of edges that contain it. H is k-regular if every vertex has the same degree k.

My question is: If we reduce a k-regular hypergraph to a general graph by replacing each edge with a clique, then the resulted general graph is not of bounded degree (the degree of a vertex can be up to n-1 where n is the total number of vertices). However I think it must be a special type of graph, I cannot figure out which type it is.

If you can help me out here I'd really appreciate it. A hypergraph $$H = (V,E)$$ consists of a set $$V = \{v_1, v_2, \cdots, v_n\}$$ of vertices and a set $$E = \{e_1, e_2, \cdots , e_m\}$$ of edges, each being a subset of $$V$$. If each $$|V| = 2$$, H is a general graph.

The degree $$d(v)$$ of a vertex v is the number of edges that contain it. H is k-regular if every vertex has the same degree k.

My question is: If we reduce a k-regular hypergraph to a general graph by replacing each edge with a clique, then the resulted general graph is not of bounded degree (the degree of a vertex can be up to n-1 where n is the total number of vertices). However I think it must be a special type of graph, I cannot figure out which type it is.

If you can help me out here I'd really appreciate it. A hypergraph $$H = (V,E)$$ consists of a set $$V = \{v_1, v_2, \cdots, v_n\}$$ of vertices and a set $$E = \{e_1, e_2, \cdots , e_m\}$$ of edges, each being a subset of $$V$$. If each $$|V| = 2$$, H is a general graph.

The degree $$d(v)$$ of a vertex v is the number of edges that contain it. H is k-regular if every vertex has the same degree k.

My question is: If we reduce a k-regular hypergraph to a general graph by replacing each edge with a clique, then the resulted general graph is not of bounded degree (the degree of a vertex can be up to n-1 where n is the total number of vertices). However I think it must be a special type of graph, I cannot figure out which type it is.

If you can help me out here I'd really appreciate it.

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# why type is the graph reduced from boundedk-regular hypergraph? A hypergraph $$H = (V,E)$$ consists of a set $$V = \{v_1, v_2, \cdots, v_n\}$$ of vertices and a set $$E = \{e_1, e_2, \cdots , e_m\}$$ of edges, each being a subset of $$V$$. If each $$|V| = 2$$, H is a general graph.

The degree $$d(v)$$ of a vertex v is the number of edges that contain it. H is boundedk-regular if every vertex has the same degree k.

My question is: If we reduce a boundedk-regular hypergraph to a general graph by replacing each edge with a clique, then the resulted general graph is not of bounded degree (the degree of a vertex can be up to n-1 where n is the total number of vertices). However I think it must be a special type of graph, I cannot figure out which type it is.

If you can help me out here I'd really appreciate it.

# why type is the graph reduced from bounded hypergraph? A hypergraph $$H = (V,E)$$ consists of a set $$V = \{v_1, v_2, \cdots, v_n\}$$ of vertices and a set $$E = \{e_1, e_2, \cdots , e_m\}$$ of edges, each being a subset of $$V$$. If each $$|V| = 2$$, H is a general graph.

The degree $$d(v)$$ of a vertex v is the number of edges that contain it. H is bounded if every vertex has the same degree k.

My question is: If we reduce a bounded hypergraph to a general graph by replacing each edge with a clique, then the resulted general graph is not bounded. However I think it must be a special type of graph, I cannot figure out which type it is.

If you can help me out here I'd really appreciate it.

# why type is the graph reduced from k-regular hypergraph? A hypergraph $$H = (V,E)$$ consists of a set $$V = \{v_1, v_2, \cdots, v_n\}$$ of vertices and a set $$E = \{e_1, e_2, \cdots , e_m\}$$ of edges, each being a subset of $$V$$. If each $$|V| = 2$$, H is a general graph.

The degree $$d(v)$$ of a vertex v is the number of edges that contain it. H is k-regular if every vertex has the same degree k.

My question is: If we reduce a k-regular hypergraph to a general graph by replacing each edge with a clique, then the resulted general graph is not of bounded degree (the degree of a vertex can be up to n-1 where n is the total number of vertices). However I think it must be a special type of graph, I cannot figure out which type it is.

If you can help me out here I'd really appreciate it.

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