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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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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?
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 ...
108 views

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 ...
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?
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 ...
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 ...
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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