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The λ-backbone colorings of graphs with tree backbones
a Combinatorial Mathematics Research Division, Institut Teknologi Bandung, Indonesia
[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]The λ-backbone coloring is one of the various problems of vertex colorings in graphs. Given an integer λ ≥ 2, a graph G = (V, E), and a spanning subgraph (backbone) H = (V, EH) of G, a λ-backbone coloring of (G, H) is a proper vertex coloring V → {1, 2,…} of G in which the colors assigned to adjacent vertices in H differ by at least λ. The λ-backbone coloring number BBCλ(G, H) of (G, H) is the smallest positive integer l for which there exists a λ-backbone coloring f : V → {1, 2,…, l} of (G, H). For a graph G with chromatic number χ(G) = k, the λ-backbone coloring number is denoted by BBCλ(G(k), H). In this paper, we consider λ-backbone colorings of graphs with tree backbones. We determine the relation between χ(G) and BBCλ(G(k), H) of (G, H) with a tree backbone H for λ ≥ 3.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text]λ-backbone coloring,λ-backbone coloring number,Chromatic number,Tree backbone[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]