A Larger Family of Planar Graphs that Satisfy the Total Coloring Conjecture |
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Authors: | Maxfield Leidner |
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Affiliation: | 1. University of Louisville, Louisville, KY, 40292, USA
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Abstract: | The article shrinks the Δ = 6 hole that exists in the family of planar graphs which satisfy the total coloring conjecture. Let G be a planar graph. If ${v_n^k}$ represents the number of vertices of degree n which lie on k distinct 3-cycles, for ${n, k in mathbb{N}}$ , then the conjecture is true for planar graphs which satisfy ${v_5^4 +2(v_5^{5^+} +v_6^4) +3v_6^5 +4v_6^{6^+} < 24}$ . |
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