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    Title: 史納克圖形的有向圈雙重覆蓋及圓流數
    Other Titles: Oriented circuit double cover and circular flow number of flower snark
    Authors: 王志維;Wang, Zhi-Wei
    Contributors: 淡江大學數學學系碩士班
    潘志實;Pan, Zhi-Shi
    Keywords: ;史納克;圈雙重覆蓋;色數;circuit;snark;circuit double cover;colouring
    Date: 2014
    Issue Date: 2015-05-01 16:11:14 (UTC+8)
    Abstract: C是G中的有向圈所形成的集合,其中C是G的有向圈雙重覆蓋,我們將
    C當成頂點集合,記為I_C,如果|C∩C''|=k則我們稱C和C''這兩個有向圈為k-連通。
    令ϕ^*_c(G)=min{χ_c(I_C)},其中ϕ_c^*(G)是所有有向圈雙重覆蓋著色數中最小的那個,非常容易證明對於所有的圖G,ϕ_c(G)<ϕ_c^*(G)。
    同時我們也在此說明存在圖G使得ϕ_c(G)<ϕ_c^*(G)。
    令J_(2k+1)是一個史納克圖形,頂點集合V(J_(2k+1) )={a_i,b_i,c_i,d_i:i=0,1,…,2k}
    邊集合E(J_(2k+1) )={b_i a_i,b_i c_i,b_i d_i,a_i a_(i+1),c_i d_(i+1),d_i c_(i+1):i=0,1,…,2k},其中每一個索引要模2k+1。
    在本篇論文中,我們證明了:
    (1)If k≥1, then χ_c(I_C )≥5.
    For a set C of directed crcuits of a graph G that form an oriented circuit double cover,we denote by I_C the graph with vertex set C,in which two circuits C and C'' are connected by k edges if |C∩C''|=k.
    Let ϕ^*_c (G)=min{χ_c(I_C)},where the minimum is taken over all the oriented circuit double covers of G,it is easy to show that for any graph G,ϕ_c(G)<ϕ^*_c (G).
    We also show that there are graphs G for which ϕ_c (G)<ϕ^*_c (G).
    Let J_(2k+1) be the flower snark which has vertex set V(J_(2k+1) )={a_i,b_i,c_i,d_i:i=0,1,…,2k}
    and dege set E(J_(2k+1) )={b_i a_i,b_i c_i,b_i d_i,a_i a_(i+1),c_i d_(i+1),d_i c_(i+1):i=0,1,…,2k},where the summationin indices are modulo 2k+1.
    In this thesis,we proved that
    (1)If k≥1, then 〖 χ〗_c (I_C )≥5.
    Appears in Collections:[數學學系暨研究所] 學位論文

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