0
votes
4answers
108 views

about the structure of components of tensor product if more than one bipartite graph is taken

I was reading about tensor product of graphs. We know that if we take tensor product of n graphs and want this product to be a connected graph then at most one graph should be bipartite. In the book ...
32
votes
6answers
2k views

Is it easy to produce hard-to-color graphs?

This question arises from my recent visit to my daughter's second-grade class, where I led some discussion and activities on graph coloring (see Math for seven-year-olds). In one such activity, each ...
13
votes
1answer
630 views

Is every graph the center of some other graph?

The center of a graph $G$ is the set of vertices that minimize the largest distance to vertices in $G$, e.g., in the graph below, that radius is $4$:           Define the ...
2
votes
1answer
94 views

Subdividing toward a unit distance graph in the plane

I just want to ask, what is the significance of subdividing a graph toward a unit distance graph? I have seen several studies of it but I cannot find what its importance. I mean, like the study of ...
1
vote
1answer
413 views

Graph Theory and Subgraphs [closed]

Let T = (V , E) be a tree with |V | = n ≥ 2. How many distinct paths are there (as sub graphs) in T? I already have the answer to this question as (n/2). The problem that I'm having is finding ...
1
vote
1answer
249 views

Distance between vertices in a vertex transitive graphs. [closed]

Can anybody help me in finding out the distances between vertices in a vertex transitive graphs. Is there any specific formula to calculate distance between vertices in this graph. Thanks for your ...
0
votes
0answers
127 views

A good upper bound on the size of k-biclique in random bipartite graphs.

Let $G = (X \cup Y, E)$ be a random bipartite graph, where $X$ and $Y$ are the set of vertices and $E$ the set of edges. I want to find an upper bound of the largest biclique in which exactly $k$ ...
0
votes
1answer
116 views

expected size of unbalanced biclique in random bipartite graph

I am discovering random graph and I am trying to prove the following result. This is a follow-up on a previous question of mine what's an upper bound on the size of the largest biclique in random ...
3
votes
1answer
134 views

what's an upper bound on the size of the largest biclique in random bipartite graph?

I am not an expert in random graph but I need the following result and I couldn't find any reference on this. Let $G(X \cup Y,p)$ be a random bipartite graph where the set of edges is $X \cup Y$, $X$ ...
8
votes
1answer
362 views

Die-rolling Hamiltonian cycles

Let $R$ be a rectangular region of the integer lattice $\mathbb{Z}^2$, each of whose unit squares is labeled with a number in $\lbrace 1, 2, 3, 4, 5, 6 \rbrace$. Say that such a labeled $R$ is ...
2
votes
1answer
607 views

Decomposition of a complete graph into maximal matching subgraphs

Is there a general way to decompose a complete graph $K_n$ into an union of maximal matching subgraphs such that no two subgraphs share an edge? For example, consider $K_4$ with vertices ...