<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>

      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.

      Filter by
      Sorted by
      Tagged with
      2
      votes
      1answer
      37 views

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

      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 ...
      5
      votes
      0answers
      48 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?
      3
      votes
      0answers
      37 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 ...
      1
      vote
      0answers
      20 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 ...
      1
      vote
      1answer
      33 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 ...
      1
      vote
      1answer
      42 views

      Rank and edges in a combinatorial graph?

      Fix a $d\in\mathbb N$ and consider the matrix $M\in\{0,1\}^{2^d\times d}$ of all $0/1$ vectors of length $d$. Consider the matrix $G\in\{0,1\}^{n\times n}$ whose $ij$ the entry is $0$ if inner product ...
      0
      votes
      0answers
      49 views

      Automorphism group of the cycle graph with $k$ diagonals

      Let $C_n$ be the cycle graph on $n$ vertices. Then $Aut(C_n) \cong D_{2n}$ the dihedral group of order $n$. Now, let $C_{n,i}$ be the cycle graph with $i$ many diagonals connecting opposite vertices ...
      1
      vote
      0answers
      22 views

      Practical calculation of minimum weight vertex-disjoint cycle covers

      How are minimum-weight vertex-disjoint cycle covers of large dense symmetric graphs actually calculated in actual implementations? I know that the problem can be reduced to general matching by ...
      0
      votes
      1answer
      49 views

      Maping of subcubes of a $(d+k)$-hypercube onto subcubes of $d$-hypercube

      Denote by $Q_n$ the n-dimensional hypercube. A vertex of $Q_n$ is represented by a vector of $n$ $\{0,1\}$-bits. An edge corresponding to two vertices whose vectors differ in one coordinate is ...
      1
      vote
      1answer
      138 views

      What is the maximal number of triangles in a planar graph?

      What is the maximal number of triangles in a planar graph with $n$ points? Here by triangle I mean any closed path of length 3 (so a triangle can also include in the interior points other than the ...
      3
      votes
      2answers
      103 views

      Avoiding multiply covered vertices in graph edge coverings

      Let $G=(V,E)$ be a simple, undirected graph with $\bigcup = E$ (that is, there are no isolated vertices). We say that $C\subseteq E$ is an edge cover of $G$ if $\bigcup C = V$. For any edge cover $C$ ...
      -1
      votes
      0answers
      93 views

      Chromatic polynomial of a bipartite graph replaced by a new graph

      Consider a semi-regular bipartite graph $C$ consisting of two parts $A$ (having each vertex of degree $\Delta$) and $B$ (having each vertex of degree $2$). Let its chromatic polynomial be $C(x)$. Now,...
      0
      votes
      0answers
      55 views

      Proving Vizing's and Brooks' theorem using the polynomial approach

      It is known that the graph polynomial defined by $\prod_{i<j}(x_i-x_j)$ where the vertices $x_k\ \ , \ \ k=\{1,2\ldots,n\}$ are ordered with respect to some order; can be used to verify the proper ...
      0
      votes
      0answers
      23 views

      Product of edge monomials and chromatic number

      As a continuation of this question and as stated in the comments, I wish to ask if the minimum value of $rad$ for all monomials equals the chromatic number when the number of variables in a monomial ...
      4
      votes
      1answer
      113 views

      Graphs with Hermitian Unitary Edge Weights

      Very recently, Hao Huang proved the Sensitivity Conjecture, which had been open for 30 years or so. Huang's proof is surprisingly short and easy. Here is Huang's preprint, a discussion on Scott ...

      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>

              新时时官网 罗马时时彩官方网站 3d和值尾振幅图中彩网 福利彩票六加一 山东时时是什么东西 北京pk走势图软件 手机捕鱼送分可提现金 福建时时网 安徽时时直播开奖结果查询 时时缩水方法