{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,4]],"date-time":"2026-09-04T21:23:12Z","timestamp":1788556992365,"version":"build-2803163510"},"reference-count":13,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,8,9]],"date-time":"2023-08-09T00:00:00Z","timestamp":1691539200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,8,9]],"date-time":"2023-08-09T00:00:00Z","timestamp":1691539200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Combinatorica"],"published-print":{"date-parts":[[2024,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Extending the idea from the recent paper by Carbonero, Hompe, Moore, and Spirkl, for every function <jats:inline-formula><jats:alternatives><jats:tex-math>$$f:\\mathbb {N}\\rightarrow \\mathbb {N}\\cup \\{\\infty \\}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>f<\/mml:mi>\n                    <mml:mo>:<\/mml:mo>\n                    <mml:mi>N<\/mml:mi>\n                    <mml:mo>\u2192<\/mml:mo>\n                    <mml:mi>N<\/mml:mi>\n                    <mml:mo>\u222a<\/mml:mo>\n                    <mml:mo>{<\/mml:mo>\n                    <mml:mi>\u221e<\/mml:mi>\n                    <mml:mo>}<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> with <jats:inline-formula><jats:alternatives><jats:tex-math>$$f(1)=1$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>f<\/mml:mi>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                    <mml:mo>)<\/mml:mo>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$f(n)\\geqslant \\left( {\\begin{array}{c}3n+1\\\\ 3\\end{array}}\\right) $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>f<\/mml:mi>\n                    <mml:mrow>\n                      <mml:mo>(<\/mml:mo>\n                      <mml:mi>n<\/mml:mi>\n                      <mml:mo>)<\/mml:mo>\n                    <\/mml:mrow>\n                    <mml:mo>\u2a7e<\/mml:mo>\n                    <mml:mfenced>\n                      <mml:mrow>\n                        <mml:mtable>\n                          <mml:mtr>\n                            <mml:mtd>\n                              <mml:mrow>\n                                <mml:mn>3<\/mml:mn>\n                                <mml:mi>n<\/mml:mi>\n                                <mml:mo>+<\/mml:mo>\n                                <mml:mn>1<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:mtd>\n                          <\/mml:mtr>\n                          <mml:mtr>\n                            <mml:mtd>\n                              <mml:mrow>\n                                <mml:mrow\/>\n                                <mml:mn>3<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:mtd>\n                          <\/mml:mtr>\n                        <\/mml:mtable>\n                      <\/mml:mrow>\n                    <\/mml:mfenced>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, we construct a hereditary class of graphs <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathcal {G}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>G<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> such that the maximum chromatic number of a graph in <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathcal {G}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>G<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> with clique number <jats:italic>n<\/jats:italic> is equal to <jats:italic>f<\/jats:italic>(<jats:italic>n<\/jats:italic>) for every <jats:inline-formula><jats:alternatives><jats:tex-math>$$n\\in \\mathbb {N}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>n<\/mml:mi>\n                    <mml:mo>\u2208<\/mml:mo>\n                    <mml:mi>N<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. In particular, we prove that there exist hereditary classes of graphs that are <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\chi $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03c7<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-bounded but not polynomially <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\chi $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03c7<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-bounded.<\/jats:p>","DOI":"10.1007\/s00493-023-00054-3","type":"journal-article","created":{"date-parts":[[2023,8,9]],"date-time":"2023-08-09T07:01:46Z","timestamp":1691564506000},"page":"1-8","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Separating Polynomial $$\\chi $$-Boundedness from $$\\chi $$-Boundedness"],"prefix":"10.1007","volume":"44","author":[{"given":"Marcin","family":"Bria\u0144ski","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"James","family":"Davies","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bartosz","family":"Walczak","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,8,9]]},"reference":[{"key":"54_CR1","doi-asserted-by":"crossref","unstructured":"Bria\u0144ski, M., Davies, J., Walczak, B.: Separating polynomial $$\\chi $$-boundedness from $$\\chi $$-boundedness, arXiv:2201.08814v1, (2022)","DOI":"10.1007\/s00493-023-00054-3"},{"key":"54_CR2","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1016\/j.jctb.2022.09.001","volume":"158","author":"A Carbonero","year":"2023","unstructured":"Carbonero, A., Hompe, P., Moore, B., Spirkl, S.: A counterexample to a conjecture about triangle-free induced subgraphs of graphs with large chromatic number. 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