A Better Lower Bound on Average Degree of 4-List-Critical Graphs
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چکیده
منابع مشابه
A Better Lower Bound on Average Degree of 4-List-Critical Graphs
This short note proves that every incomplete k-list-critical graph has average degree at least k − 1 + k−3 k2−2k+2 . This improves the best known bound for k = 4, 5, 6. The same bound holds for online k-list-critical graphs.
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We improve the best known bounds on the average degree of online k-list-critical graphs for k > 6. Specifically, for k > 7 we show that every non-complete online k-list-critical graph has average degree at least k−1+ (k−3) 2(2k−3) k4−2k3−11k2+28k−14 and every non-complete online 6-list-critical graph has average degree at least 5 + 93 766 . The same bounds hold for offline k-list-critical graphs.
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The concept of average degree-eccentricity matrix ADE(G) of a connected graph $G$ is introduced. Some coefficients of the characteristic polynomial of ADE(G) are obtained, as well as a bound for the eigenvalues of ADE(G). We also introduce the average degree-eccentricity graph energy and establish bounds for it.
متن کاملImproved lower bounds on the number of edges in list critical and online list critical graphs
We prove that every k-list-critical graph (k ≥ 7) on n ≥ k + 2 vertices has at least 1 2 ( k − 1 + k−3 (k−c)(k−1)+k−3 ) n edges where c = (k − 3) ( 1 2 − 1 (k−1)(k−2) ) . This improves the bound established by Kostochka and Stiebitz [13]. The same bound holds for online k-list-critical graphs, improving the bound established by Riasat and Schauz [16]. Both bounds follow from a more general resu...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2016
ISSN: 1077-8926
DOI: 10.37236/5971