• 제목/요약/키워드: graph polytope

검색결과 8건 처리시간 0.019초

COMPUTATION OF TOTAL CHROMATIC NUMBER FOR CERTAIN CONVEX POLYTOPE GRAPHS

  • A. PUNITHA;G. JAYARAMAN
    • Journal of applied mathematics & informatics
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    • 제42권3호
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    • pp.567-582
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    • 2024
  • A total coloring of a graph G is an assignment of colors to the elements of a graphs G such that no adjacent vertices and edges receive the same color. The total chromatic number of a graph G , denoted by χ''(G), is the minimum number of colors that suffice in a total coloring. In this paper, we proved the Behzad and Vizing conjecture for certain convex polytope graphs Dpn, Qpn, Rpn, En, Sn, Gn, Tn, Un, Cn,respectively. This significant result in a graph G contributes to the advancement of graph theory and combinatorics by further confirming the conjecture's applicability to specific classes of graphs. The presented proof of the Behzad and Vizing conjecture for certain convex polytope graphs not only provides theoretical insights into the structural properties of graphs but also has practical implications. Overall, this paper contributes to the advancement of graph theory and combinatorics by confirming the validity of the Behzad and Vizing conjecture in a graph G and establishing its relevance to applied problems in sciences and engineering.

VOLUME OF GRAPH POLYTOPES FOR THE PATH-STAR TYPE GRAPHS

  • Ju, Hyeong-Kwan;Seo, Soo-Jeong
    • 호남수학학술지
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    • 제38권1호
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    • pp.71-84
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    • 2016
  • The aim of this work is to compute the volume of the graph polytope associated with various type of finite simple graphs composed of paths and stars. Recurrence relations are obtained using the recursive volume formula (RVF) which was introduced in Lee and Ju ([3]). We also discussed the relationship between the volume of the graph polytopes and the number of linear extensions of the associated posets for given bipartite graphs.

DIFFERENT VOLUME COMPUTATIONAL METHODS OF GRAPH POLYTOPES

  • Ju, Hyeong-Kwan;Kim, Sangwook;Lee, Daeseok
    • 대한수학회보
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    • 제55권5호
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    • pp.1405-1417
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    • 2018
  • The aim of this work is to introduce several different volume computational methods of graph polytopes associated with various types of finite simple graphs. Among them, we obtained the recursive volume formula (RVF) that is fundamental and most useful to compute the volume of the graph polytope for an arbitrary finite simple graph.

Polytope와 graph에 관하여 (On polytopes and graphs)

  • 김연식
    • 한국수학교육학회지시리즈A:수학교육
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    • 제10권2호
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    • pp.4-8
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    • 1972
  • We consider the class (equation omitted) of all k-degenerate graphs, for k a non-negative integer. The class (equation omitted) and (equation omitted) are exactly the classes of totally disconnected graphs and of forests, respectively; the classes (equation omitted) and (equation omitted) properly contain all outerplanar and planar graphs respectively. The advantage of this view point is that many of the known results for chromatic number and point arboricity have natural extensions, for all larger values of k. The purpose of this note is to show that a graph G is (P$^3$)-realizable if G is planar and 3-degenerate.

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이분할성 우선순위제약을 갖는 배낭문제에 대한 다면체적 절단평면 (Facets of Knapsack Polytopes with Bipartite Precedence Constraints)

  • 이경식;박성수;박경철
    • 한국경영과학회지
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    • 제23권4호
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    • pp.1-10
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    • 1998
  • We consider the precedence-constrained knapsack problem. which is a knapsack problem with precedence constraints imposed on the set of variables. Especially, we focus on the case where the precedence constraints cir be represented as a bipartite graph, which occurs most frequently in applications. Based on the previous studios for the general case, we specialize the polyhedral results on the related polytope and derive stronger results on the facet-defining properties of the inequalities.

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LINEAR EXTENSIONS OF DIAMOND POSETS

  • Ju, Hyeong-Kwan;Seo, Seunghyun
    • 호남수학학술지
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    • 제41권4호
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    • pp.863-870
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    • 2019
  • In this paper, we obtain the enumeration results on the number of linear extensions of diamond posets. We find the recurrence relations and exponential generating functions for the number of linear extensions of diamond posets. We also get some results for the volume of graph polytope associated with bipartite graphs which are underlying graphs of diamond posets.