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        Questions tagged [graph-theory]

        Questions about the branch of combinatorics called graph theory (not to be used for questions concerning the graph of a function). This tag can be further specialized via using it in combination with more specialized tags such as extremal-graph-theory, spectral-graph-theory, algebraic-graph-theory, topological-graph-theory, random-graphs, graph-colorings and several others.

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        1answer
        132 views

        Quotient graph of a tree

        We know that every graph is isomorphic to a subgraph of a complete graph. Similarly, can we say that every graph is isomorphic to a quotient graph of a tree?
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        1answer
        57 views

        Combining three matchings to form a maximal matching

        Consider a regular tripartite graph $G$ with maximum degree $\Delta\ge3$ and parts $A,B,C$. Now, the induced subgraphs $A\cup B, B\cup C$ and $A\cup C$ are all bipartite. Now, is there a way to ...
        1
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        1answer
        108 views

        Number formation and bridged graphs, connection or coincidence?

        Bridged graphs sequence $g(n) =$ "Number of simple connected bridged graphs on $n+2$ nodes". We have $g(n)=1, 3, 10, 52, 351, 3714,\dots$ from A052446. Number formation sequence We also have $f(n) ...
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        1answer
        67 views

        Minimizing the number of segments in drawings of planar graphs

        Every planar graph has at most $3n-6$ edges, where $n$ is the number of vertices. Moreover, every planar graph can be drawn with straight-line edges in the plane, without crossings. For example, for ...
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        0answers
        128 views

        Research-level blogs on complex networks:

        I'm an applied mathematician that has a research interest in complex networks for modelling biological systems and I wondered whether the MathOverflow community might know of research-level blogs that ...
        2
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        1answer
        61 views

        On sum of elements in products of matrices for a simple graph

        Let $G$ be a simple graph with vertex set $\{v_1,v_2,\ldots,v_n\}$. The adjacency matrix of $G$ is the 0-1 matrix $A$, where $A_{i,j}=1$ when $v_i$ is adjacent with $v_j$. The degree matrix is the ...
        1
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        1answer
        50 views

        The Total Graph is similar to a line graph

        Consider the total graph of a regular graph. From the structure, it seems that it has a similar structure to the line graph ( two different sub-cliques joining at a single point) except that, in ...
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        1answer
        73 views

        Significance of the Eigenvalues of the adjacency matrix of a weighted di-graph

        I'm currently running a simulation on a bunch of randomly generated points, each with two randomly selected 'partners' from the set of points. In the simulation the points try to move such that they ...
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        0answers
        76 views

        Vertex in a graph whose stabilizer (in a given group $\Gamma$ of automorphisms) does not fix any neighbour vertex?

        I know next to nothing about graph theory, but I did recently use the concept of graphs and groups acting on them to formalize the proof of a statement that has a priori nothing to do with graphs. I ...
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        0answers
        65 views

        Zero-One law for Hamiltonian path subgraphs of Hamming Distance Graphs?

        $(\alpha,\beta,d)$-Hamming Distance Graph $G_d(\alpha,\beta)$ for $\alpha,\beta\in(0,1]$ is a graph on $2^d$ vertices $v_0,\dots,v_{2^d-1}$ with edges $(v_i,v_j)\in\mathcal E(G_d)$ iff $0<\sum_{t=1}...
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        1answer
        52 views

        Chromatic Polynomial when two disjoint graphs are joined at $2$ distinct points [closed]

        Consider a graph with chromatic polynomial $P(x)$ joined to a clique of order $k$ in two distinct points (joining here just means interesection of points). Then, what is the chromatic polynomial of ...
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        0answers
        68 views

        An upper bound on the minimum number of vertices in a girth 5 graph of chromatic number $k$

        Is there a known upper bound on the minimum number of vertices in a graph with girth 5 and chromatic number $k$? Could you also give references for this?
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        0answers
        49 views

        Can the vertices of a planar graph of min degree 3 be covered with edges of average weight ( sum of degrees) at most 14?

        Consider a planar graph where every vertex is incident to at least 3 edges, and assign to each edge a weight equal to the sum of the degrees of its endpoints. If not, what is the smallest n so that ...
        2
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        0answers
        25 views

        Counterpart of dominating sets in graphs

        A $t$-fold dominating set in a simple undirected graph $G$ with vertex set $V$ is a subset $D\subseteq V$ such that each vertex of $V\setminus D$ has at least $t$ neighbours in $D$. I am interested ...
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        1answer
        39 views

        Induced subgraphs of the line graph of a dense linear hypergraph

        Given a hypergraph $H=(V,E)$ we associate to it its line graph $L(H)$ given by $V(L(H)) =E$ and $$E(L(H)) = \big\{\{e_1,e_2\}: e_1\neq e_2 \in E \text{ and } e_1\cap e_2 \neq \emptyset \big\}.$$ We ...

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