Results 41 to 50 of about 44,462 (291)
General Vertex-Distinguishing Total Coloring of Graphs
Journal of Applied Mathematics, 2014 The general vertex-distinguishing total chromatic number of a graph G is the minimum integer k, for which the vertices and edges of G are colored using k colors such that any two vertices have distinct sets of colors of them and their incident edges.
Chanjuan Liu, Enqiang Zhu
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Planar graphs with $\Delta \geq 7$ and no triangle adjacent to a $C_4$ are minimally edge and total choosable [PDF]
Discrete Mathematics & Theoretical Computer Science, 2016 For planar graphs, we consider the problems of list edge coloring and list total coloring. Edge coloring is the problem of coloring the edges while ensuring that two edges that are adjacent receive different colors.
Marthe Bonamy +2 more
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Exploring Relationship Between Traditional Lattices and Graph Lattices of Topological Coding
Jisuanji kexue yu tansuo, 2021 It is known that there are no polynomial quantum algorithms to solve some lattice difficult problems. Uncolored graphic lattice and colored graphic lattice are the products of multidisciplinary intersection inspired by lattice theory. A uncolored graphic
ZHANG Mingjun, YANG Sihua, YAO Bing
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A study of the total coloring of graphs. [PDF]
, 2012 The area of total coloring is a more recent and less studied area than vertex and edge coloring, but recently, some attention has been given to the Total Coloring Conjecture, which states that each graph\u27s total chromatic number xT is no greater than ...
Leidner, Maxfield Edwin
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Odd-Graceful Total Colorings for Constructing Graphic Lattice
Mathematics, 2021 The security of passwords generated by the graphic lattices is based on the difficulty of the graph isomorphism, graceful tree conjecture, and total coloring conjecture.
Jing Su, Hui Sun, Bing Yao
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Oriented Total-Coloring of Oriented Graphs [PDF]
, 2022 A proper $n$-coloring of a graph $G$ is an assignment of colors from $\{1,\ldots,n\}$ to its vertices such that no two adjacent vertices get assigned the same color. The chromatic number of $G$, denoted by $\chi(G)$, refers to the smallest $n$ such that $
Nandy, Ayan +6 more
core
Generalized total colorings of graphs
Discussiones Mathematicae Graph Theory, 2011 An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphism. Let P and Q be additive hereditary properties of graphs. A (P ,Q)-total coloring ∗Research supported in part by Slovak VEGA Grant 2/0194/10. 210 M. Borowiecki, A. Kemnitz, M. Marangio and P.
Mieczyslaw Borowiecki +3 more
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International Journal of Mathematics and Mathematical Sciences, 2017 Let G be a graph and ϕ:V(G)∪E(G)→{1,2,3,…,k} be a k-total coloring. Let w(v) denote the sum of color on a vertex v and colors assigned to edges incident to v.
Patcharapan Jumnongnit +1 more
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Total colorings of equibipartite graphs
Discrete Mathematics, 1999 The total chromatic number \(\chi_T(G)\) of a (simple) graph \(G\) is the least number of colours needed to colour the vertices and edges of \(G\) such that no two adjacent or incident vertices/edges receive the same colour. It is known that if \(G\) is a bipartite graph, then \(\Delta(G)+ 1\leq\chi_T(G)\leq \Delta(G)+ 2\), where \(\Delta(G)\) is the ...
Bor-Liang Chen +3 more
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Pediatric Blood &Cancer, EarlyView.ABSTRACT Background Survival after relapse in pediatric acute myeloid leukemia (AML) remains poor, highlighting the critical importance of identifying prognostic factors to guide optimal relapse management. Methods We investigated the prognostic impact of multiparameter flow cytometry (MFC) measurable residual disease (MRD) in 188 patients with first ...
Camilla Poulsen +21 more
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