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Vertex-Distinguishing IE-Total Colorings of Complete Bipartite Graphs Km,N(m < n) [PDF]
Discussiones Mathematicae Graph Theory, 2013 Let G be a simple graph. An IE-total coloring f of G is a coloring of the vertices and edges of G so that no two adjacent vertices receive the same color. Let C(u) be the set of colors of vertex u and edges incident to u under f. For an IE-total coloring
Chen Xiang’en, Gao Yuping, Yao Bing
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Deciding the On-line Chromatic Number of a Graph with Pre-Coloring is PSPACE-Complete [PDF]
, 2014 The problem of determining if the on-line chromatic number of a graph is less than or equal to k, given a pre-coloring, is shown to be PSPACE ...
Kudahl, Christian
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A special machine for solving NP-complete problems [PDF]
Fundamental ResearchA specialized computer named as the Electronic Probe Computer (EPC) has been developed to address large-scale NP-complete problems. The EPC employs a hybrid serial/parallel computational model, structured around four main subsystems: a converting system,
Jin Xu +13 more
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On Incidence Coloring of Complete Multipartite and Semicubic Bipartite Graphs
Discussiones Mathematicae Graph Theory, 2018 In the paper, we show that the incidence chromatic number χi of a complete k-partite graph is at most Δ + 2 (i.e., proving the incidence coloring conjecture for these graphs) and it is equal to Δ + 1 if and only if the smallest part has only one vertex ...
Janczewski Robert +2 more
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Difference of Facial Achromatic Numbers between Two Triangular Embeddings of a Graph
Theory and Applications of Graphs, 2023 A facial $3$-complete $k$-coloring of a triangulation $G$ on a surface is a vertex $k$-coloring such that every triple of $k$-colors appears on the boundary of some face of $G$.
Kengo Enami, Yumiko Ohno
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A hyperedge coloring and application in combinatorial testing
AKCE International Journal of Graphs and Combinatorics, 2022 For a hypergraph H, a uniform k-coloring of hyperedges always has the same (to within 1) number of hyperedges of each color, whereas an equitable k-coloring of hyperedges has the property that at every vertex all the colors incident the same number of ...
Yasmeen Akhtar
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Solving Graph Coloring Problem Based on Grover Algorithm [PDF]
Jisuanji kexue, 2023 Grover quantum search algorithm is a famous quantum algorithm designed for unstructured search problems.It can be used to solve problems such as graph coloring and shortest path sorting,and can also effectively decipher cryptosystems.Graph coloring ...
LIU Xiaonan, LIU Zhengyu, XIE Haoshan, ZHAO Chenyan
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Graph theoretic and algorithmic aspect of the equitable coloring problem in block graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 An equitable coloring of a graph $G=(V,E)$ is a (proper) vertex-coloring of $G$, such that the sizes of any two color classes differ by at most one. In this paper, we consider the equitable coloring problem in block graphs.
Hanna Furmańczyk, Vahan Mkrtchyan
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A Note on the Equitable Choosability of Complete Bipartite Graphs
Discussiones Mathematicae Graph Theory, 2021 In 2003 Kostochka, Pelsmajer, and West introduced a list analogue of equitable coloring called equitable choosability. A k-assignment, L, for a graph G assigns a list, L(v), of k available colors to each v ∈ V (G), and an equitable L-coloring of G is a ...
Mudrock Jeffrey A. +4 more
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AKCE International Journal of Graphs and Combinatorics, 2023 We introduce a concept in graph coloring motivated by the popular Sudoku puzzle. Let [Formula: see text] be a graph of order n with chromatic number [Formula: see text] and let [Formula: see text] Let [Formula: see text] be a k-coloring of the induced ...
J. Maria Jeyaseeli +3 more
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