Do any two spanning trees of a simple graph always have some common edges?











up vote
1
down vote

favorite












I tried few cases and found any two spanning tree of a simple graph has some common edges. I mean I couldn't find any counter example so far. But I couldn't prove or disprove this either. How to prove or disprove this conjecture?










share|cite|improve this question






















  • Assuming the weights of the graph are distinct, the edge with the minimum weight will be present in all the minimum spanning trees.
    – Gokul
    1 hour ago










  • @Gokul minimum spanning tree? What?...
    – Mr. Sigma.
    34 mins ago










  • Oh, apologies. I read the title as whether minimum spanning tree have common edges.
    – Gokul
    28 mins ago















up vote
1
down vote

favorite












I tried few cases and found any two spanning tree of a simple graph has some common edges. I mean I couldn't find any counter example so far. But I couldn't prove or disprove this either. How to prove or disprove this conjecture?










share|cite|improve this question






















  • Assuming the weights of the graph are distinct, the edge with the minimum weight will be present in all the minimum spanning trees.
    – Gokul
    1 hour ago










  • @Gokul minimum spanning tree? What?...
    – Mr. Sigma.
    34 mins ago










  • Oh, apologies. I read the title as whether minimum spanning tree have common edges.
    – Gokul
    28 mins ago













up vote
1
down vote

favorite









up vote
1
down vote

favorite











I tried few cases and found any two spanning tree of a simple graph has some common edges. I mean I couldn't find any counter example so far. But I couldn't prove or disprove this either. How to prove or disprove this conjecture?










share|cite|improve this question













I tried few cases and found any two spanning tree of a simple graph has some common edges. I mean I couldn't find any counter example so far. But I couldn't prove or disprove this either. How to prove or disprove this conjecture?







graphs graph-theory spanning-trees






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked 1 hour ago









Mr. Sigma.

348116




348116












  • Assuming the weights of the graph are distinct, the edge with the minimum weight will be present in all the minimum spanning trees.
    – Gokul
    1 hour ago










  • @Gokul minimum spanning tree? What?...
    – Mr. Sigma.
    34 mins ago










  • Oh, apologies. I read the title as whether minimum spanning tree have common edges.
    – Gokul
    28 mins ago


















  • Assuming the weights of the graph are distinct, the edge with the minimum weight will be present in all the minimum spanning trees.
    – Gokul
    1 hour ago










  • @Gokul minimum spanning tree? What?...
    – Mr. Sigma.
    34 mins ago










  • Oh, apologies. I read the title as whether minimum spanning tree have common edges.
    – Gokul
    28 mins ago
















Assuming the weights of the graph are distinct, the edge with the minimum weight will be present in all the minimum spanning trees.
– Gokul
1 hour ago




Assuming the weights of the graph are distinct, the edge with the minimum weight will be present in all the minimum spanning trees.
– Gokul
1 hour ago












@Gokul minimum spanning tree? What?...
– Mr. Sigma.
34 mins ago




@Gokul minimum spanning tree? What?...
– Mr. Sigma.
34 mins ago












Oh, apologies. I read the title as whether minimum spanning tree have common edges.
– Gokul
28 mins ago




Oh, apologies. I read the title as whether minimum spanning tree have common edges.
– Gokul
28 mins ago










2 Answers
2






active

oldest

votes

















up vote
2
down vote













No, it's not true that any two spanning trees of a graph have common edges.



Consider the wheel graph:



enter image description here



You can make a spanning tree with edges "inside" the loop and another one from the outer loop.






share|cite|improve this answer




























    up vote
    2
    down vote













    No, consider the complete graph $K_4$:



    It has the following edge-disjoint spanning trees:
    enter image description here






    share|cite|improve this answer



















    • 1




      Oh! Elegant. Why I couldn't come upon this solution. ':O.
      – Mr. Sigma.
      4 mins ago











    Your Answer





    StackExchange.ifUsing("editor", function () {
    return StackExchange.using("mathjaxEditing", function () {
    StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
    StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
    });
    });
    }, "mathjax-editing");

    StackExchange.ready(function() {
    var channelOptions = {
    tags: "".split(" "),
    id: "419"
    };
    initTagRenderer("".split(" "), "".split(" "), channelOptions);

    StackExchange.using("externalEditor", function() {
    // Have to fire editor after snippets, if snippets enabled
    if (StackExchange.settings.snippets.snippetsEnabled) {
    StackExchange.using("snippets", function() {
    createEditor();
    });
    }
    else {
    createEditor();
    }
    });

    function createEditor() {
    StackExchange.prepareEditor({
    heartbeatType: 'answer',
    convertImagesToLinks: false,
    noModals: true,
    showLowRepImageUploadWarning: true,
    reputationToPostImages: null,
    bindNavPrevention: true,
    postfix: "",
    imageUploader: {
    brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
    contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
    allowUrls: true
    },
    onDemand: true,
    discardSelector: ".discard-answer"
    ,immediatelyShowMarkdownHelp:true
    });


    }
    });














    draft saved

    draft discarded


















    StackExchange.ready(
    function () {
    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fcs.stackexchange.com%2fquestions%2f101038%2fdo-any-two-spanning-trees-of-a-simple-graph-always-have-some-common-edges%23new-answer', 'question_page');
    }
    );

    Post as a guest















    Required, but never shown

























    2 Answers
    2






    active

    oldest

    votes








    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    2
    down vote













    No, it's not true that any two spanning trees of a graph have common edges.



    Consider the wheel graph:



    enter image description here



    You can make a spanning tree with edges "inside" the loop and another one from the outer loop.






    share|cite|improve this answer

























      up vote
      2
      down vote













      No, it's not true that any two spanning trees of a graph have common edges.



      Consider the wheel graph:



      enter image description here



      You can make a spanning tree with edges "inside" the loop and another one from the outer loop.






      share|cite|improve this answer























        up vote
        2
        down vote










        up vote
        2
        down vote









        No, it's not true that any two spanning trees of a graph have common edges.



        Consider the wheel graph:



        enter image description here



        You can make a spanning tree with edges "inside" the loop and another one from the outer loop.






        share|cite|improve this answer












        No, it's not true that any two spanning trees of a graph have common edges.



        Consider the wheel graph:



        enter image description here



        You can make a spanning tree with edges "inside" the loop and another one from the outer loop.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered 26 mins ago









        Gokul

        241110




        241110






















            up vote
            2
            down vote













            No, consider the complete graph $K_4$:



            It has the following edge-disjoint spanning trees:
            enter image description here






            share|cite|improve this answer



















            • 1




              Oh! Elegant. Why I couldn't come upon this solution. ':O.
              – Mr. Sigma.
              4 mins ago















            up vote
            2
            down vote













            No, consider the complete graph $K_4$:



            It has the following edge-disjoint spanning trees:
            enter image description here






            share|cite|improve this answer



















            • 1




              Oh! Elegant. Why I couldn't come upon this solution. ':O.
              – Mr. Sigma.
              4 mins ago













            up vote
            2
            down vote










            up vote
            2
            down vote









            No, consider the complete graph $K_4$:



            It has the following edge-disjoint spanning trees:
            enter image description here






            share|cite|improve this answer














            No, consider the complete graph $K_4$:



            It has the following edge-disjoint spanning trees:
            enter image description here







            share|cite|improve this answer














            share|cite|improve this answer



            share|cite|improve this answer








            edited 22 mins ago

























            answered 28 mins ago









            Bjørn Kjos-Hanssen

            23417




            23417








            • 1




              Oh! Elegant. Why I couldn't come upon this solution. ':O.
              – Mr. Sigma.
              4 mins ago














            • 1




              Oh! Elegant. Why I couldn't come upon this solution. ':O.
              – Mr. Sigma.
              4 mins ago








            1




            1




            Oh! Elegant. Why I couldn't come upon this solution. ':O.
            – Mr. Sigma.
            4 mins ago




            Oh! Elegant. Why I couldn't come upon this solution. ':O.
            – Mr. Sigma.
            4 mins ago


















            draft saved

            draft discarded




















































            Thanks for contributing an answer to Computer Science Stack Exchange!


            • Please be sure to answer the question. Provide details and share your research!

            But avoid



            • Asking for help, clarification, or responding to other answers.

            • Making statements based on opinion; back them up with references or personal experience.


            Use MathJax to format equations. MathJax reference.


            To learn more, see our tips on writing great answers.





            Some of your past answers have not been well-received, and you're in danger of being blocked from answering.


            Please pay close attention to the following guidance:


            • Please be sure to answer the question. Provide details and share your research!

            But avoid



            • Asking for help, clarification, or responding to other answers.

            • Making statements based on opinion; back them up with references or personal experience.


            To learn more, see our tips on writing great answers.




            draft saved


            draft discarded














            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fcs.stackexchange.com%2fquestions%2f101038%2fdo-any-two-spanning-trees-of-a-simple-graph-always-have-some-common-edges%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown





















































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown

































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown







            Popular posts from this blog

            Eastern Orthodox Church

            Zagreb

            Understanding the information contained in the Deep Space Network XML data?