<em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

    <em id="zlul0"></em>

      <dl id="zlul0"></dl>
        <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
        <em id="zlul0"></em>

        <div id="zlul0"><ol id="zlul0"></ol></div>

        All Questions

        Filter by
        Sorted by
        Tagged with
        3
        votes
        2answers
        109 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 $C$ ...
        -2
        votes
        2answers
        171 views

        Cardinality of a set of mutually disjoint perfect matchings of $K_\omega$

        If $G=(V,E)$ is a simple, undirected graph, we say that $M\subseteq E$ is a perfect matching if the members of $M$ are pairwise disjoint and $\bigcup M = V$. Let $K_\omega$ be the complete graph on $\...
        2
        votes
        1answer
        118 views

        Chromatic number of the linear graph on $[\omega]^\omega$

        Let $[\omega]^\omega$ denote the set of infinite subsets of $\omega$. Let $$E = \{\{a,b\}: a,b\in [\omega]^\omega\text{ and } |a\cap b| = 1\}.$$ It is clear that $G = ([\omega]^\omega, E)$ has no ...
        5
        votes
        3answers
        162 views

        Disjunction number of a graph

        Let $S\neq \emptyset$ be a set. We make its powerset ${\cal P}(S)$ into a simple, undirected graph by saying that $A, B\in{\cal P}(S)$ form an edge if and only if $A\cap B=\emptyset$. The ...
        1
        vote
        1answer
        78 views

        Maximizing “happy” vertices in splitting an infinite graph

        This question is motivated by a real life task (which is briefly described after the question.) Let $G=(V,E)$ be an infinite graph. For $v\in V$ let $N(v) = \{x\in V: \{v,x\}\in E\}$. If $S\subseteq ...
        1
        vote
        0answers
        71 views

        Generalization of the linear extension theorem to directed acyclic graphs

        Using Zorn's lemma one can prove a generalization of the order extension theorem, that states any acyclic digraph is always contained in another acyclic unilaterally connected digraph on the same ...
        0
        votes
        1answer
        74 views

        Linear intersection number and chromatic number for infinite graphs

        Given a hypergraph $H=(V,E)$ we let its intersection graph $I(H)$ be defined by $V(I(H)) = E$ and $E(I(H)) = \{\{e,e'\}: (e\neq e'\in E) \land (e\cap e'\neq \emptyset)\}$. A linear hypergraph is a ...
        3
        votes
        1answer
        209 views

        Does every directed graph have a directed coloring with $4$ colors?

        Every finite directed graph has a majority coloring with $4$ colors. (The notion of majority coloring is defined below.) Question. Can every infinite directed graph be majority-colored with $4$ ...
        2
        votes
        1answer
        141 views

        Induced minors of $\{0,1\}^\omega$

        Let $G=(V,E)$ be a simple, undirected graph. Suppose that ${\cal S}$ is a collection of non-empty, connected, and pairwise disjoint subsets of $V$. Let $G({\cal S})$ be the graph with vertex set ${\...
        -1
        votes
        1answer
        77 views

        Finding a good transversal basis

        A hypergraph $H=(V,E)$ consists of an non-empty set $V$ and a collection $E\subseteq {\cal P}(V)\setminus \{\emptyset\}$ of non-empty subsets of $V$. A transversal of $H$ is a set $T\subseteq V$ such ...
        0
        votes
        1answer
        85 views

        Connected infinite graphs in which all matchings are “small”

        Is there a countable, simple, connected graph $G=(\omega, E)$ such that $\text{deg}(v)$ is infinite for all $v\in \omega$, and for all matchings $M\subseteq E$ the set $V\setminus (\bigcup M)$ is ...
        12
        votes
        1answer
        390 views

        Is each cover of the plane by lines minimizable?

        A cover $\mathcal C$ of a set $X$ by subsets of $X$ is called $\bullet$ minimal if for every $C\in\mathcal C$ the family $\mathcal C\setminus\{C\}$ is not a cover of $X$; $\bullet$ minimizable if $\...
        34
        votes
        2answers
        4k views

        How to find Erd?s' treasure trove?

        The renowned mathematician, Paul Erd?s, has published more than 1500 papers in various branches of mathematics including discrete mathematics, graph theory, number theory, mathematical analysis, ...
        5
        votes
        1answer
        164 views

        “König's theorem” for $T_2$-spaces?

        For any topological space $(X,\tau)$ we define a matching to be a collection of non-empty and pairwise disjoint open sets. We define the matching number $\nu(X,\tau)$ to be the smallest cardinal $\...
        1
        vote
        2answers
        178 views

        Bipartite subgraphs with lots of edges

        Suppose $G=(V,E)$ is a simple, undirected graph with $|V|,|E|$ infinite. Is there $B\subseteq E$ with $|B| = |E|$ such that $(V,B)$ is bipartite?

        15 30 50 per page
        山西福彩快乐十分钟
          <em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

          <em id="zlul0"></em>

            <dl id="zlul0"></dl>
              <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
              <em id="zlul0"></em>

              <div id="zlul0"><ol id="zlul0"></ol></div>
                <em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

                <em id="zlul0"></em>

                  <dl id="zlul0"></dl>
                    <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
                    <em id="zlul0"></em>

                    <div id="zlul0"><ol id="zlul0"></ol></div>
                    南京站街女性息 胆大包天开过什么生肖 重庆时时彩几时开 pk10全天计划网页2期班 pk10稳赚技巧数据多高 美女人体艺术摄影 重庆肘时彩官网 奥地利秒速时时开奖 老重庆时时开彩结果360 赛车北京pk10网站