<ruby id="d9npn"></ruby>

      <sub id="d9npn"><progress id="d9npn"></progress></sub>

      <nobr id="d9npn"></nobr>

      <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

      <th id="d9npn"><meter id="d9npn"></meter></th>

      Stack Exchange Network

      Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

      Visit Stack Exchange

      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.

      2
      votes
      0answers
      43 views

      Are contraction-sensitive graphs necessarily vertex-transitive?

      We say that a finite, simple, undirected graph $G=(V,E)$ is contraction-sensitive if collapsing any $2$ non-adjacent points increases the Hadwiger number. An example of such a graph is the icosahedron....
      2
      votes
      2answers
      92 views

      Does any long path in a planar graph contain one of O(n) k-tuple of vertices?

      My question is a bit related to both the container method and shallow cell complexity. Let's start with that the number of length $\ell$ paths (where $\ell$ denotes the number of vertices of the path!)...
      2
      votes
      0answers
      37 views
      +50

      Does the bounded branching/log depth dihotomy hold for rooted trees?

      Let $T$ be a rooted tree. For any subtree $T' \subset T$ define its leaf-weight $lw$ as the number of leaves of $T'$. Further, for $T' \subset T$ define the branch-depth of a node $v \in T'$ as the ...
      2
      votes
      0answers
      48 views

      Reference request: $n$-edge-coloring bipartite graph $K_{n,n}$ such that monochromatic parts are isomorphic

      I am finding references for the following problem: We call a $n\times n$ 0-1 matrix permutation if there are exactly one $1$ in each row/column. Suppose $A$ is a 0-1 matrix of size $n\times n$ in ...
      3
      votes
      1answer
      74 views

      Ear decompositions and spanning trees

      I am looking for a reference for the following theorem: Theorem: Let $G$ be a 2-connected, simple, undirected graph, and let $T$ be a spanning tree. Then $G$ has an ear decomposition in which every ...
      5
      votes
      1answer
      143 views

      Which groups contain a comb?

      The comb is the undirected simple graph with nodes $\mathbb{N} \times \mathbb{N}$ where $\mathbb{N} \ni 0$ and edges $$ \{\{(m,n), (m,n+1)\}, \{(m,0), (m+1,0)\} \;|\; m \in \mathbb{N}, n \in \mathbb{N}...
      0
      votes
      1answer
      66 views

      Contracting non-adjacent points in the icosahedron

      Are there $2$ non-adjacent points in the icosahedron graph $G$ such that contracting them leaves the Hadwiger number unchanged?
      3
      votes
      1answer
      124 views

      When can any graph $G$ be expressed as a union of $\alpha(G)$ complete graphs?

      If for any graph $H$ we define $\alpha(H)$ to be the cardinality of any maximum size indepedent set in $H$. Then under what conditions can any graph $G$ be expressed as a union of $\alpha(G)$ complete ...
      -1
      votes
      0answers
      30 views

      Bipartite allocation with minimum cost

      Given two vertex sets $V_1$ and $V_2$. The vertices in $V_2$ have a limitation on the maximum degree of each vertex being $K$. I need to find an allocation algorithm such that every pair of vertices ...
      1
      vote
      1answer
      65 views

      Expected size of matchings in a cubic graph

      Let $G$ be a random cubic graph on $n$ vertices. Let $M$ be the set of (not necessarily maximum) matchings of $G$. What is the expected size (i.e. number of edges) of an element of $M$? In other ...
      1
      vote
      1answer
      83 views

      Find large “induced” bipartite graph in a dense graph?

      Do there exist constants $d>0$, $0<c<1$, $\delta>0$ so that for all large $n$, there exists a graph $H$ satisfying $$e_H\ge dn^2,$$ and then no matter how we remove some edges from $H$ to ...
      1
      vote
      0answers
      25 views

      Succinct circuits and NEXPTIME-complete problems

      I am fascinated by a recent fact I was reading: Succinct Circuits are simple machines used to descibe graphs in exponentially less space, which leads to the downside that solving a problem on that ...
      2
      votes
      0answers
      41 views

      Fastest Algorithm to calculate Graph pebbling number?

      I am interested in Graph Pebbling, and in particular what are the fastest known algorithm is to find the pebbling number of a graph. Also, i am interested whether there are lower limits on the runtime ...
      1
      vote
      0answers
      26 views

      Algorithms for Detecting the Completion of a Triangle in a Stream of Edges

      I need to efficiently determine in a complete weighted graph $G$ the sequence of triangles according to descending order of circumferences. My idea would be to incrementally construct a new graph $...
      1
      vote
      0answers
      74 views

      Are all even regular undirected Cayley graphs of Class 1?

      Are even order Cayley graphs of Class 1, that is, can they be edge-colored with exactly $m$ colors, where $m$ is the degree of each vertex? I think yes, because of the symmetry the Cayley graphs ...

      15 30 50 per page
      特码生肖图
      <ruby id="d9npn"></ruby>

          <sub id="d9npn"><progress id="d9npn"></progress></sub>

          <nobr id="d9npn"></nobr>

          <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

          <th id="d9npn"><meter id="d9npn"></meter></th>

          <ruby id="d9npn"></ruby>

              <sub id="d9npn"><progress id="d9npn"></progress></sub>

              <nobr id="d9npn"></nobr>

              <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

              <th id="d9npn"><meter id="d9npn"></meter></th>