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

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enter image description hereenter image description here 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.

enter image description hereA 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.

enter image description here 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?

enter image description hereA 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?

enter image description hereA 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?

enter image description hereA 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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